RKHS regression with Gaussian kernel

RKHS regression with Gaussian kernel

Usage

morie_rkhs_full(x, y, markers, h = NULL, lam = 1)

Arguments

x

Fixed-effect design.

y

Numeric response.

markers

Genotype matrix (n x m).

h

Kernel bandwidth (default median ||m_i - m_j||^2).

lam

Ridge regulariser on alpha (default 1).

Value

list(estimate, alpha, beta, K, f_hat, se, h, n, method).

References

Gianola & van Kaam (2008). Montesinos Lopez Ch 5.

Examples

morie_rkhs_full(x = rnorm(50), y = rnorm(50), markers = matrix(sample(0:2, 200, TRUE), 50, 4))
#> $estimate
#> [1] 0.01500975
#> 
#> $alpha
#>  [1]  0.4422937316  0.6189520720 -0.7516815570 -0.6868373597  1.6064375218
#>  [6]  2.2790574369 -0.0215422652 -1.3480623999 -0.3991672935  0.6846941334
#> [11] -1.0306340259  0.6863331357  0.0003430805 -0.7967217585 -0.2625076679
#> [16]  0.0489096527  1.1214681062 -0.9171553460 -1.5011551352 -0.4584782973
#> [21]  0.6364968810  0.2291925916 -0.9428566644 -0.7892912071 -0.5131261582
#> [26]  0.7830095123  0.1838479578 -0.0607484656 -0.3748911218  1.4360584032
#> [31]  1.7487182348  0.2137765860  0.2750919726 -0.5454456747 -1.0092000222
#> [36] -1.2516996137 -2.6310032263  0.3831852330 -0.0305150164  1.7632323794
#> [41] -0.0195372899  1.3245921535  0.2478062340  0.2935240711  0.4087704424
#> [46] -0.8790972925  0.5136092976 -0.1912354471 -1.8648684461  0.5975702873
#> 
#> $beta
#>        X1        X2 
#> 0.1281334 0.2326268 
#> 
#> $K
#>             [,1]      [,2]       [,3]       [,4]       [,5]       [,6]
#>  [1,] 1.00000000 0.3678794 0.07427358 0.16529889 0.36787944 0.09071795
#>  [2,] 0.36787944 1.0000000 0.30119421 0.30119421 0.30119421 0.36787944
#>  [3,] 0.07427358 0.3011942 1.00000000 0.44932896 0.20189652 0.81873075
#>  [4,] 0.16529889 0.3011942 0.44932896 1.00000000 0.09071795 0.36787944
#>  [5,] 0.36787944 0.3011942 0.20189652 0.09071795 1.00000000 0.16529889
#>  [6,] 0.09071795 0.3678794 0.81873075 0.36787944 0.16529889 1.00000000
#>  [7,] 0.54881164 0.6703200 0.30119421 0.30119421 0.67032005 0.24659696
#>  [8,] 0.24659696 0.4493290 0.30119421 0.13533528 0.30119421 0.54881164
#>  [9,] 0.30119421 0.8187308 0.16529889 0.16529889 0.16529889 0.30119421
#> [10,] 0.30119421 0.8187308 0.16529889 0.16529889 0.16529889 0.30119421
#> [11,] 0.54881164 0.6703200 0.13533528 0.13533528 0.30119421 0.24659696
#> [12,] 0.67032005 0.5488116 0.24659696 0.54881164 0.24659696 0.30119421
#> [13,] 0.36787944 0.3011942 0.30119421 0.67032005 0.13533528 0.36787944
#> [14,] 0.67032005 0.5488116 0.24659696 0.54881164 0.24659696 0.30119421
#> [15,] 0.36787944 0.2018965 0.30119421 0.30119421 0.30119421 0.36787944
#> [16,] 0.67032005 0.3678794 0.24659696 0.24659696 0.54881164 0.30119421
#> [17,] 0.36787944 0.2018965 0.30119421 0.30119421 0.30119421 0.36787944
#> [18,] 0.30119421 0.8187308 0.36787944 0.36787944 0.36787944 0.30119421
#> [19,] 0.16529889 0.3011942 0.44932896 1.00000000 0.09071795 0.36787944
#> [20,] 0.54881164 0.6703200 0.30119421 0.30119421 0.67032005 0.24659696
#> [21,] 0.30119421 0.5488116 0.16529889 0.36787944 0.07427358 0.30119421
#> [22,] 0.36787944 1.0000000 0.30119421 0.30119421 0.30119421 0.36787944
#> [23,] 0.24659696 0.3011942 0.67032005 0.67032005 0.30119421 0.54881164
#> [24,] 0.30119421 0.1652989 0.16529889 0.16529889 0.16529889 0.30119421
#> [25,] 0.20189652 0.8187308 0.36787944 0.16529889 0.36787944 0.44932896
#> [26,] 0.30119421 0.8187308 0.54881164 0.54881164 0.24659696 0.67032005
#> [27,] 0.30119421 0.3678794 0.54881164 0.54881164 0.24659696 0.67032005
#> [28,] 0.16529889 0.3011942 0.67032005 0.30119421 0.30119421 0.81873075
#> [29,] 0.36787944 0.1353353 0.20189652 0.44932896 0.20189652 0.16529889
#> [30,] 0.67032005 0.8187308 0.24659696 0.24659696 0.54881164 0.30119421
#> [31,] 0.30119421 0.2465970 0.36787944 0.81873075 0.16529889 0.30119421
#> [32,] 0.44932896 0.5488116 0.54881164 0.54881164 0.54881164 0.44932896
#> [33,] 0.81873075 0.3011942 0.09071795 0.20189652 0.44932896 0.07427358
#> [34,] 0.67032005 0.2465970 0.16529889 0.36787944 0.36787944 0.13533528
#> [35,] 0.44932896 0.8187308 0.16529889 0.36787944 0.16529889 0.20189652
#> [36,] 0.67032005 0.3678794 0.16529889 0.16529889 0.81873075 0.13533528
#> [37,] 0.09071795 0.3678794 0.81873075 0.36787944 0.16529889 1.00000000
#> [38,] 0.36787944 0.6703200 0.09071795 0.20189652 0.09071795 0.16529889
#> [39,] 0.16529889 0.1353353 0.44932896 0.20189652 0.44932896 0.36787944
#> [40,] 0.07427358 0.3011942 0.44932896 0.20189652 0.09071795 0.81873075
#> [41,] 0.24659696 0.3011942 0.67032005 0.67032005 0.30119421 0.54881164
#> [42,] 0.30119421 0.5488116 0.36787944 0.81873075 0.16529889 0.30119421
#> [43,] 0.36787944 0.3011942 0.20189652 0.09071795 1.00000000 0.16529889
#> [44,] 0.36787944 0.3011942 0.20189652 0.09071795 1.00000000 0.16529889
#> [45,] 0.13533528 0.3678794 0.81873075 0.81873075 0.16529889 0.67032005
#> [46,] 0.67032005 0.3678794 0.16529889 0.16529889 0.81873075 0.13533528
#> [47,] 0.30119421 0.3678794 0.54881164 0.54881164 0.24659696 0.67032005
#> [48,] 0.13533528 0.2465970 0.36787944 0.16529889 0.16529889 0.67032005
#> [49,] 0.30119421 0.5488116 0.16529889 0.36787944 0.07427358 0.30119421
#> [50,] 0.16529889 0.4493290 0.67032005 0.67032005 0.13533528 0.81873075
#>            [,7]      [,8]       [,9]      [,10]     [,11]     [,12]     [,13]
#>  [1,] 0.5488116 0.2465970 0.30119421 0.30119421 0.5488116 0.6703200 0.3678794
#>  [2,] 0.6703200 0.4493290 0.81873075 0.81873075 0.6703200 0.5488116 0.3011942
#>  [3,] 0.3011942 0.3011942 0.16529889 0.16529889 0.1353353 0.2465970 0.3011942
#>  [4,] 0.3011942 0.1353353 0.16529889 0.16529889 0.1353353 0.5488116 0.6703200
#>  [5,] 0.6703200 0.3011942 0.16529889 0.16529889 0.3011942 0.2465970 0.1353353
#>  [6,] 0.2465970 0.5488116 0.30119421 0.30119421 0.2465970 0.3011942 0.3678794
#>  [7,] 1.0000000 0.3011942 0.36787944 0.36787944 0.4493290 0.5488116 0.3011942
#>  [8,] 0.3011942 1.0000000 0.54881164 0.54881164 0.6703200 0.3678794 0.3011942
#>  [9,] 0.3678794 0.5488116 1.00000000 1.00000000 0.8187308 0.4493290 0.2465970
#> [10,] 0.3678794 0.5488116 1.00000000 1.00000000 0.8187308 0.4493290 0.2465970
#> [11,] 0.4493290 0.6703200 0.81873075 0.81873075 1.0000000 0.5488116 0.3011942
#> [12,] 0.5488116 0.3678794 0.44932896 0.44932896 0.5488116 1.0000000 0.8187308
#> [13,] 0.3011942 0.3011942 0.24659696 0.24659696 0.3011942 0.8187308 1.0000000
#> [14,] 0.5488116 0.3678794 0.44932896 0.44932896 0.5488116 1.0000000 0.8187308
#> [15,] 0.3011942 0.4493290 0.16529889 0.16529889 0.3011942 0.5488116 0.6703200
#> [16,] 0.5488116 0.5488116 0.30119421 0.30119421 0.5488116 0.6703200 0.5488116
#> [17,] 0.3011942 0.4493290 0.16529889 0.16529889 0.3011942 0.5488116 0.6703200
#> [18,] 0.8187308 0.2465970 0.44932896 0.44932896 0.3678794 0.4493290 0.2465970
#> [19,] 0.3011942 0.1353353 0.16529889 0.16529889 0.1353353 0.5488116 0.6703200
#> [20,] 1.0000000 0.3011942 0.36787944 0.36787944 0.4493290 0.5488116 0.3011942
#> [21,] 0.2465970 0.3678794 0.67032005 0.67032005 0.5488116 0.6703200 0.5488116
#> [22,] 0.6703200 0.4493290 0.81873075 0.81873075 0.6703200 0.5488116 0.3011942
#> [23,] 0.4493290 0.3011942 0.16529889 0.16529889 0.2018965 0.5488116 0.6703200
#> [24,] 0.1652989 0.5488116 0.20189652 0.20189652 0.3678794 0.4493290 0.5488116
#> [25,] 0.5488116 0.5488116 0.67032005 0.67032005 0.5488116 0.3011942 0.1652989
#> [26,] 0.5488116 0.5488116 0.67032005 0.67032005 0.5488116 0.6703200 0.5488116
#> [27,] 0.3678794 0.5488116 0.30119421 0.30119421 0.3678794 0.6703200 0.8187308
#> [28,] 0.3011942 0.6703200 0.24659696 0.24659696 0.3011942 0.3678794 0.4493290
#> [29,] 0.3011942 0.1353353 0.07427358 0.07427358 0.1353353 0.5488116 0.6703200
#> [30,] 0.8187308 0.5488116 0.67032005 0.67032005 0.8187308 0.6703200 0.3678794
#> [31,] 0.3678794 0.1652989 0.13533528 0.13533528 0.1652989 0.6703200 0.8187308
#> [32,] 0.8187308 0.3678794 0.30119421 0.30119421 0.3678794 0.6703200 0.5488116
#> [33,] 0.6703200 0.1353353 0.16529889 0.16529889 0.3011942 0.5488116 0.3011942
#> [34,] 0.5488116 0.1652989 0.13533528 0.13533528 0.2465970 0.6703200 0.5488116
#> [35,] 0.5488116 0.2465970 0.67032005 0.67032005 0.5488116 0.6703200 0.3678794
#> [36,] 0.8187308 0.2465970 0.20189652 0.20189652 0.3678794 0.4493290 0.2465970
#> [37,] 0.2465970 0.5488116 0.30119421 0.30119421 0.2465970 0.3011942 0.3678794
#> [38,] 0.3011942 0.3011942 0.81873075 0.81873075 0.6703200 0.5488116 0.3011942
#> [39,] 0.3011942 0.3011942 0.07427358 0.07427358 0.1353353 0.2465970 0.3011942
#> [40,] 0.1353353 0.6703200 0.36787944 0.36787944 0.3011942 0.2465970 0.3011942
#> [41,] 0.4493290 0.3011942 0.16529889 0.16529889 0.2018965 0.5488116 0.6703200
#> [42,] 0.5488116 0.1652989 0.30119421 0.30119421 0.2465970 0.6703200 0.5488116
#> [43,] 0.6703200 0.3011942 0.16529889 0.16529889 0.3011942 0.2465970 0.1353353
#> [44,] 0.6703200 0.3011942 0.16529889 0.16529889 0.3011942 0.2465970 0.1353353
#> [45,] 0.3678794 0.2465970 0.20189652 0.20189652 0.1652989 0.4493290 0.5488116
#> [46,] 0.8187308 0.2465970 0.20189652 0.20189652 0.3678794 0.4493290 0.2465970
#> [47,] 0.3678794 0.5488116 0.30119421 0.30119421 0.3678794 0.6703200 0.8187308
#> [48,] 0.1652989 0.8187308 0.30119421 0.30119421 0.3678794 0.3011942 0.3678794
#> [49,] 0.2465970 0.3678794 0.67032005 0.67032005 0.5488116 0.6703200 0.5488116
#> [50,] 0.3011942 0.4493290 0.36787944 0.36787944 0.3011942 0.5488116 0.6703200
#>           [,14]     [,15]     [,16]     [,17]      [,18]      [,19]     [,20]
#>  [1,] 0.6703200 0.3678794 0.6703200 0.3678794 0.30119421 0.16529889 0.5488116
#>  [2,] 0.5488116 0.2018965 0.3678794 0.2018965 0.81873075 0.30119421 0.6703200
#>  [3,] 0.2465970 0.3011942 0.2465970 0.3011942 0.36787944 0.44932896 0.3011942
#>  [4,] 0.5488116 0.3011942 0.2465970 0.3011942 0.36787944 1.00000000 0.3011942
#>  [5,] 0.2465970 0.3011942 0.5488116 0.3011942 0.36787944 0.09071795 0.6703200
#>  [6,] 0.3011942 0.3678794 0.3011942 0.3678794 0.30119421 0.36787944 0.2465970
#>  [7,] 0.5488116 0.3011942 0.5488116 0.3011942 0.81873075 0.30119421 1.0000000
#>  [8,] 0.3678794 0.4493290 0.5488116 0.4493290 0.24659696 0.13533528 0.3011942
#>  [9,] 0.4493290 0.1652989 0.3011942 0.1652989 0.44932896 0.16529889 0.3678794
#> [10,] 0.4493290 0.1652989 0.3011942 0.1652989 0.44932896 0.16529889 0.3678794
#> [11,] 0.5488116 0.3011942 0.5488116 0.3011942 0.36787944 0.13533528 0.4493290
#> [12,] 1.0000000 0.5488116 0.6703200 0.5488116 0.44932896 0.54881164 0.5488116
#> [13,] 0.8187308 0.6703200 0.5488116 0.6703200 0.24659696 0.67032005 0.3011942
#> [14,] 1.0000000 0.5488116 0.6703200 0.5488116 0.44932896 0.54881164 0.5488116
#> [15,] 0.5488116 1.0000000 0.8187308 1.0000000 0.16529889 0.30119421 0.3011942
#> [16,] 0.6703200 0.8187308 1.0000000 0.8187308 0.30119421 0.24659696 0.5488116
#> [17,] 0.5488116 1.0000000 0.8187308 1.0000000 0.16529889 0.30119421 0.3011942
#> [18,] 0.4493290 0.1652989 0.3011942 0.1652989 1.00000000 0.36787944 0.8187308
#> [19,] 0.5488116 0.3011942 0.2465970 0.3011942 0.36787944 1.00000000 0.3011942
#> [20,] 0.5488116 0.3011942 0.5488116 0.3011942 0.81873075 0.30119421 1.0000000
#> [21,] 0.6703200 0.2465970 0.3011942 0.2465970 0.30119421 0.36787944 0.2465970
#> [22,] 0.5488116 0.2018965 0.3678794 0.2018965 0.81873075 0.30119421 0.6703200
#> [23,] 0.5488116 0.6703200 0.5488116 0.6703200 0.36787944 0.67032005 0.4493290
#> [24,] 0.4493290 0.8187308 0.6703200 0.8187308 0.09071795 0.16529889 0.1652989
#> [25,] 0.3011942 0.1652989 0.3011942 0.1652989 0.67032005 0.16529889 0.5488116
#> [26,] 0.6703200 0.3678794 0.4493290 0.3678794 0.67032005 0.54881164 0.5488116
#> [27,] 0.6703200 0.8187308 0.6703200 0.8187308 0.30119421 0.54881164 0.3678794
#> [28,] 0.3678794 0.6703200 0.5488116 0.6703200 0.24659696 0.30119421 0.3011942
#> [29,] 0.5488116 0.6703200 0.5488116 0.6703200 0.16529889 0.44932896 0.3011942
#> [30,] 0.6703200 0.3678794 0.6703200 0.3678794 0.67032005 0.24659696 0.8187308
#> [31,] 0.6703200 0.5488116 0.4493290 0.5488116 0.30119421 0.81873075 0.3678794
#> [32,] 0.6703200 0.5488116 0.6703200 0.5488116 0.67032005 0.54881164 0.8187308
#> [33,] 0.5488116 0.3011942 0.5488116 0.3011942 0.36787944 0.20189652 0.6703200
#> [34,] 0.6703200 0.5488116 0.6703200 0.5488116 0.30119421 0.36787944 0.5488116
#> [35,] 0.6703200 0.1652989 0.3011942 0.1652989 0.67032005 0.36787944 0.5488116
#> [36,] 0.4493290 0.3678794 0.6703200 0.3678794 0.44932896 0.16529889 0.8187308
#> [37,] 0.3011942 0.3678794 0.3011942 0.3678794 0.30119421 0.36787944 0.2465970
#> [38,] 0.5488116 0.1353353 0.2465970 0.1353353 0.36787944 0.20189652 0.3011942
#> [39,] 0.2465970 0.6703200 0.5488116 0.6703200 0.16529889 0.20189652 0.3011942
#> [40,] 0.2465970 0.3011942 0.2465970 0.3011942 0.16529889 0.20189652 0.1353353
#> [41,] 0.5488116 0.6703200 0.5488116 0.6703200 0.36787944 0.67032005 0.4493290
#> [42,] 0.6703200 0.2465970 0.3011942 0.2465970 0.67032005 0.81873075 0.5488116
#> [43,] 0.2465970 0.3011942 0.5488116 0.3011942 0.36787944 0.09071795 0.6703200
#> [44,] 0.2465970 0.3011942 0.5488116 0.3011942 0.36787944 0.09071795 0.6703200
#> [45,] 0.4493290 0.3678794 0.3011942 0.3678794 0.44932896 0.81873075 0.3678794
#> [46,] 0.4493290 0.3678794 0.6703200 0.3678794 0.44932896 0.16529889 0.8187308
#> [47,] 0.6703200 0.8187308 0.6703200 0.8187308 0.30119421 0.54881164 0.3678794
#> [48,] 0.3011942 0.5488116 0.4493290 0.5488116 0.13533528 0.16529889 0.1652989
#> [49,] 0.6703200 0.2465970 0.3011942 0.2465970 0.30119421 0.36787944 0.2465970
#> [50,] 0.5488116 0.4493290 0.3678794 0.4493290 0.36787944 0.67032005 0.3011942
#>            [,21]     [,22]     [,23]      [,24]      [,25]     [,26]     [,27]
#>  [1,] 0.30119421 0.3678794 0.2465970 0.30119421 0.20189652 0.3011942 0.3011942
#>  [2,] 0.54881164 1.0000000 0.3011942 0.16529889 0.81873075 0.8187308 0.3678794
#>  [3,] 0.16529889 0.3011942 0.6703200 0.16529889 0.36787944 0.5488116 0.5488116
#>  [4,] 0.36787944 0.3011942 0.6703200 0.16529889 0.16529889 0.5488116 0.5488116
#>  [5,] 0.07427358 0.3011942 0.3011942 0.16529889 0.36787944 0.2465970 0.2465970
#>  [6,] 0.30119421 0.3678794 0.5488116 0.30119421 0.44932896 0.6703200 0.6703200
#>  [7,] 0.24659696 0.6703200 0.4493290 0.16529889 0.54881164 0.5488116 0.3678794
#>  [8,] 0.36787944 0.4493290 0.3011942 0.54881164 0.54881164 0.5488116 0.5488116
#>  [9,] 0.67032005 0.8187308 0.1652989 0.20189652 0.67032005 0.6703200 0.3011942
#> [10,] 0.67032005 0.8187308 0.1652989 0.20189652 0.67032005 0.6703200 0.3011942
#> [11,] 0.54881164 0.6703200 0.2018965 0.36787944 0.54881164 0.5488116 0.3678794
#> [12,] 0.67032005 0.5488116 0.5488116 0.44932896 0.30119421 0.6703200 0.6703200
#> [13,] 0.54881164 0.3011942 0.6703200 0.54881164 0.16529889 0.5488116 0.8187308
#> [14,] 0.67032005 0.5488116 0.5488116 0.44932896 0.30119421 0.6703200 0.6703200
#> [15,] 0.24659696 0.2018965 0.6703200 0.81873075 0.16529889 0.3678794 0.8187308
#> [16,] 0.30119421 0.3678794 0.5488116 0.67032005 0.30119421 0.4493290 0.6703200
#> [17,] 0.24659696 0.2018965 0.6703200 0.81873075 0.16529889 0.3678794 0.8187308
#> [18,] 0.30119421 0.8187308 0.3678794 0.09071795 0.67032005 0.6703200 0.3011942
#> [19,] 0.36787944 0.3011942 0.6703200 0.16529889 0.16529889 0.5488116 0.5488116
#> [20,] 0.24659696 0.6703200 0.4493290 0.16529889 0.54881164 0.5488116 0.3678794
#> [21,] 1.00000000 0.5488116 0.2465970 0.30119421 0.30119421 0.6703200 0.4493290
#> [22,] 0.54881164 1.0000000 0.3011942 0.16529889 0.81873075 0.8187308 0.3678794
#> [23,] 0.24659696 0.3011942 1.0000000 0.36787944 0.24659696 0.5488116 0.8187308
#> [24,] 0.30119421 0.1652989 0.3678794 1.00000000 0.13533528 0.3011942 0.6703200
#> [25,] 0.30119421 0.8187308 0.2465970 0.13533528 1.00000000 0.6703200 0.3011942
#> [26,] 0.67032005 0.8187308 0.5488116 0.30119421 0.67032005 1.0000000 0.6703200
#> [27,] 0.44932896 0.3678794 0.8187308 0.67032005 0.30119421 0.6703200 1.0000000
#> [28,] 0.24659696 0.3011942 0.6703200 0.54881164 0.36787944 0.5488116 0.8187308
#> [29,] 0.16529889 0.1353353 0.6703200 0.36787944 0.07427358 0.2465970 0.5488116
#> [30,] 0.44932896 0.8187308 0.3678794 0.30119421 0.67032005 0.6703200 0.4493290
#> [31,] 0.30119421 0.2465970 0.8187308 0.30119421 0.13533528 0.4493290 0.6703200
#> [32,] 0.30119421 0.5488116 0.8187308 0.30119421 0.44932896 0.6703200 0.6703200
#> [33,] 0.16529889 0.3011942 0.3011942 0.16529889 0.16529889 0.2465970 0.2465970
#> [34,] 0.20189652 0.2465970 0.5488116 0.30119421 0.13533528 0.3011942 0.4493290
#> [35,] 0.67032005 0.8187308 0.2465970 0.13533528 0.44932896 0.6703200 0.3011942
#> [36,] 0.13533528 0.3678794 0.3678794 0.20189652 0.30119421 0.3011942 0.3011942
#> [37,] 0.30119421 0.3678794 0.5488116 0.30119421 0.44932896 0.6703200 0.6703200
#> [38,] 0.81873075 0.6703200 0.1353353 0.16529889 0.36787944 0.5488116 0.2465970
#> [39,] 0.07427358 0.1353353 0.6703200 0.36787944 0.16529889 0.2465970 0.5488116
#> [40,] 0.36787944 0.3011942 0.3011942 0.36787944 0.36787944 0.5488116 0.5488116
#> [41,] 0.24659696 0.3011942 1.0000000 0.36787944 0.24659696 0.5488116 0.8187308
#> [42,] 0.44932896 0.5488116 0.5488116 0.13533528 0.30119421 0.6703200 0.4493290
#> [43,] 0.07427358 0.3011942 0.3011942 0.16529889 0.36787944 0.2465970 0.2465970
#> [44,] 0.07427358 0.3011942 0.3011942 0.16529889 0.36787944 0.2465970 0.2465970
#> [45,] 0.30119421 0.3678794 0.8187308 0.20189652 0.30119421 0.6703200 0.6703200
#> [46,] 0.13533528 0.3678794 0.3678794 0.20189652 0.30119421 0.3011942 0.3011942
#> [47,] 0.44932896 0.3678794 0.8187308 0.67032005 0.30119421 0.6703200 1.0000000
#> [48,] 0.30119421 0.2465970 0.3678794 0.67032005 0.30119421 0.4493290 0.6703200
#> [49,] 1.00000000 0.5488116 0.2465970 0.30119421 0.30119421 0.6703200 0.4493290
#> [50,] 0.54881164 0.4493290 0.6703200 0.36787944 0.36787944 0.8187308 0.8187308
#>           [,28]      [,29]     [,30]     [,31]     [,32]      [,33]      [,34]
#>  [1,] 0.1652989 0.36787944 0.6703200 0.3011942 0.4493290 0.81873075 0.67032005
#>  [2,] 0.3011942 0.13533528 0.8187308 0.2465970 0.5488116 0.30119421 0.24659696
#>  [3,] 0.6703200 0.20189652 0.2465970 0.3678794 0.5488116 0.09071795 0.16529889
#>  [4,] 0.3011942 0.44932896 0.2465970 0.8187308 0.5488116 0.20189652 0.36787944
#>  [5,] 0.3011942 0.20189652 0.5488116 0.1652989 0.5488116 0.44932896 0.36787944
#>  [6,] 0.8187308 0.16529889 0.3011942 0.3011942 0.4493290 0.07427358 0.13533528
#>  [7,] 0.3011942 0.30119421 0.8187308 0.3678794 0.8187308 0.67032005 0.54881164
#>  [8,] 0.6703200 0.13533528 0.5488116 0.1652989 0.3678794 0.13533528 0.16529889
#>  [9,] 0.2465970 0.07427358 0.6703200 0.1353353 0.3011942 0.16529889 0.13533528
#> [10,] 0.2465970 0.07427358 0.6703200 0.1353353 0.3011942 0.16529889 0.13533528
#> [11,] 0.3011942 0.13533528 0.8187308 0.1652989 0.3678794 0.30119421 0.24659696
#> [12,] 0.3678794 0.54881164 0.6703200 0.6703200 0.6703200 0.54881164 0.67032005
#> [13,] 0.4493290 0.67032005 0.3678794 0.8187308 0.5488116 0.30119421 0.54881164
#> [14,] 0.3678794 0.54881164 0.6703200 0.6703200 0.6703200 0.54881164 0.67032005
#> [15,] 0.6703200 0.67032005 0.3678794 0.5488116 0.5488116 0.30119421 0.54881164
#> [16,] 0.5488116 0.54881164 0.6703200 0.4493290 0.6703200 0.54881164 0.67032005
#> [17,] 0.6703200 0.67032005 0.3678794 0.5488116 0.5488116 0.30119421 0.54881164
#> [18,] 0.2465970 0.16529889 0.6703200 0.3011942 0.6703200 0.36787944 0.30119421
#> [19,] 0.3011942 0.44932896 0.2465970 0.8187308 0.5488116 0.20189652 0.36787944
#> [20,] 0.3011942 0.30119421 0.8187308 0.3678794 0.8187308 0.67032005 0.54881164
#> [21,] 0.2465970 0.16529889 0.4493290 0.3011942 0.3011942 0.16529889 0.20189652
#> [22,] 0.3011942 0.13533528 0.8187308 0.2465970 0.5488116 0.30119421 0.24659696
#> [23,] 0.6703200 0.67032005 0.3678794 0.8187308 0.8187308 0.30119421 0.54881164
#> [24,] 0.5488116 0.36787944 0.3011942 0.3011942 0.3011942 0.16529889 0.30119421
#> [25,] 0.3678794 0.07427358 0.6703200 0.1353353 0.4493290 0.16529889 0.13533528
#> [26,] 0.5488116 0.24659696 0.6703200 0.4493290 0.6703200 0.24659696 0.30119421
#> [27,] 0.8187308 0.54881164 0.4493290 0.6703200 0.6703200 0.24659696 0.44932896
#> [28,] 1.0000000 0.30119421 0.3678794 0.3678794 0.5488116 0.13533528 0.24659696
#> [29,] 0.3011942 1.00000000 0.2465970 0.8187308 0.5488116 0.44932896 0.81873075
#> [30,] 0.3678794 0.24659696 1.0000000 0.3011942 0.6703200 0.54881164 0.44932896
#> [31,] 0.3678794 0.81873075 0.3011942 1.0000000 0.6703200 0.36787944 0.67032005
#> [32,] 0.5488116 0.54881164 0.6703200 0.6703200 1.0000000 0.54881164 0.67032005
#> [33,] 0.1353353 0.44932896 0.5488116 0.3678794 0.5488116 1.00000000 0.81873075
#> [34,] 0.2465970 0.81873075 0.4493290 0.6703200 0.6703200 0.81873075 1.00000000
#> [35,] 0.1652989 0.16529889 0.6703200 0.3011942 0.4493290 0.36787944 0.30119421
#> [36,] 0.2465970 0.36787944 0.6703200 0.3011942 0.6703200 0.81873075 0.67032005
#> [37,] 0.8187308 0.16529889 0.3011942 0.3011942 0.4493290 0.07427358 0.13533528
#> [38,] 0.1353353 0.09071795 0.5488116 0.1652989 0.2465970 0.20189652 0.16529889
#> [39,] 0.6703200 0.44932896 0.2465970 0.3678794 0.5488116 0.20189652 0.36787944
#> [40,] 0.6703200 0.09071795 0.2465970 0.1652989 0.2465970 0.04076220 0.07427358
#> [41,] 0.6703200 0.67032005 0.3678794 0.8187308 0.8187308 0.30119421 0.54881164
#> [42,] 0.2465970 0.36787944 0.4493290 0.6703200 0.6703200 0.36787944 0.44932896
#> [43,] 0.3011942 0.20189652 0.5488116 0.1652989 0.5488116 0.44932896 0.36787944
#> [44,] 0.3011942 0.20189652 0.5488116 0.1652989 0.5488116 0.44932896 0.36787944
#> [45,] 0.5488116 0.36787944 0.3011942 0.6703200 0.6703200 0.16529889 0.30119421
#> [46,] 0.2465970 0.36787944 0.6703200 0.3011942 0.6703200 0.81873075 0.67032005
#> [47,] 0.8187308 0.54881164 0.4493290 0.6703200 0.6703200 0.24659696 0.44932896
#> [48,] 0.8187308 0.16529889 0.3011942 0.2018965 0.3011942 0.07427358 0.13533528
#> [49,] 0.2465970 0.16529889 0.4493290 0.3011942 0.3011942 0.16529889 0.20189652
#> [50,] 0.6703200 0.30119421 0.3678794 0.5488116 0.5488116 0.13533528 0.24659696
#>            [,35]      [,36]      [,37]      [,38]      [,39]      [,40]
#>  [1,] 0.44932896 0.67032005 0.09071795 0.36787944 0.16529889 0.07427358
#>  [2,] 0.81873075 0.36787944 0.36787944 0.67032005 0.13533528 0.30119421
#>  [3,] 0.16529889 0.16529889 0.81873075 0.09071795 0.44932896 0.44932896
#>  [4,] 0.36787944 0.16529889 0.36787944 0.20189652 0.20189652 0.20189652
#>  [5,] 0.16529889 0.81873075 0.16529889 0.09071795 0.44932896 0.09071795
#>  [6,] 0.20189652 0.13533528 1.00000000 0.16529889 0.36787944 0.81873075
#>  [7,] 0.54881164 0.81873075 0.24659696 0.30119421 0.30119421 0.13533528
#>  [8,] 0.24659696 0.24659696 0.54881164 0.30119421 0.30119421 0.67032005
#>  [9,] 0.67032005 0.20189652 0.30119421 0.81873075 0.07427358 0.36787944
#> [10,] 0.67032005 0.20189652 0.30119421 0.81873075 0.07427358 0.36787944
#> [11,] 0.54881164 0.36787944 0.24659696 0.67032005 0.13533528 0.30119421
#> [12,] 0.67032005 0.44932896 0.30119421 0.54881164 0.24659696 0.24659696
#> [13,] 0.36787944 0.24659696 0.36787944 0.30119421 0.30119421 0.30119421
#> [14,] 0.67032005 0.44932896 0.30119421 0.54881164 0.24659696 0.24659696
#> [15,] 0.16529889 0.36787944 0.36787944 0.13533528 0.67032005 0.30119421
#> [16,] 0.30119421 0.67032005 0.30119421 0.24659696 0.54881164 0.24659696
#> [17,] 0.16529889 0.36787944 0.36787944 0.13533528 0.67032005 0.30119421
#> [18,] 0.67032005 0.44932896 0.30119421 0.36787944 0.16529889 0.16529889
#> [19,] 0.36787944 0.16529889 0.36787944 0.20189652 0.20189652 0.20189652
#> [20,] 0.54881164 0.81873075 0.24659696 0.30119421 0.30119421 0.13533528
#> [21,] 0.67032005 0.13533528 0.30119421 0.81873075 0.07427358 0.36787944
#> [22,] 0.81873075 0.36787944 0.36787944 0.67032005 0.13533528 0.30119421
#> [23,] 0.24659696 0.36787944 0.54881164 0.13533528 0.67032005 0.30119421
#> [24,] 0.13533528 0.20189652 0.30119421 0.16529889 0.36787944 0.36787944
#> [25,] 0.44932896 0.30119421 0.44932896 0.36787944 0.16529889 0.36787944
#> [26,] 0.67032005 0.30119421 0.67032005 0.54881164 0.24659696 0.54881164
#> [27,] 0.30119421 0.30119421 0.67032005 0.24659696 0.54881164 0.54881164
#> [28,] 0.16529889 0.24659696 0.81873075 0.13533528 0.67032005 0.67032005
#> [29,] 0.16529889 0.36787944 0.16529889 0.09071795 0.44932896 0.09071795
#> [30,] 0.67032005 0.67032005 0.30119421 0.54881164 0.24659696 0.24659696
#> [31,] 0.30119421 0.30119421 0.30119421 0.16529889 0.36787944 0.16529889
#> [32,] 0.44932896 0.67032005 0.44932896 0.24659696 0.54881164 0.24659696
#> [33,] 0.36787944 0.81873075 0.07427358 0.20189652 0.20189652 0.04076220
#> [34,] 0.30119421 0.67032005 0.13533528 0.16529889 0.36787944 0.07427358
#> [35,] 1.00000000 0.30119421 0.20189652 0.81873075 0.07427358 0.16529889
#> [36,] 0.30119421 1.00000000 0.13533528 0.16529889 0.36787944 0.07427358
#> [37,] 0.20189652 0.13533528 1.00000000 0.16529889 0.36787944 0.81873075
#> [38,] 0.81873075 0.16529889 0.16529889 1.00000000 0.04076220 0.20189652
#> [39,] 0.07427358 0.36787944 0.36787944 0.04076220 1.00000000 0.20189652
#> [40,] 0.16529889 0.07427358 0.81873075 0.20189652 0.20189652 1.00000000
#> [41,] 0.24659696 0.36787944 0.54881164 0.13533528 0.67032005 0.30119421
#> [42,] 0.67032005 0.30119421 0.30119421 0.36787944 0.16529889 0.16529889
#> [43,] 0.16529889 0.81873075 0.16529889 0.09071795 0.44932896 0.09071795
#> [44,] 0.16529889 0.81873075 0.16529889 0.09071795 0.44932896 0.09071795
#> [45,] 0.30119421 0.20189652 0.67032005 0.16529889 0.36787944 0.36787944
#> [46,] 0.30119421 1.00000000 0.13533528 0.16529889 0.36787944 0.07427358
#> [47,] 0.30119421 0.30119421 0.67032005 0.24659696 0.54881164 0.54881164
#> [48,] 0.13533528 0.13533528 0.67032005 0.16529889 0.36787944 0.81873075
#> [49,] 0.67032005 0.13533528 0.30119421 0.81873075 0.07427358 0.36787944
#> [50,] 0.36787944 0.16529889 0.81873075 0.30119421 0.30119421 0.67032005
#>           [,41]     [,42]      [,43]      [,44]     [,45]      [,46]     [,47]
#>  [1,] 0.2465970 0.3011942 0.36787944 0.36787944 0.1353353 0.67032005 0.3011942
#>  [2,] 0.3011942 0.5488116 0.30119421 0.30119421 0.3678794 0.36787944 0.3678794
#>  [3,] 0.6703200 0.3678794 0.20189652 0.20189652 0.8187308 0.16529889 0.5488116
#>  [4,] 0.6703200 0.8187308 0.09071795 0.09071795 0.8187308 0.16529889 0.5488116
#>  [5,] 0.3011942 0.1652989 1.00000000 1.00000000 0.1652989 0.81873075 0.2465970
#>  [6,] 0.5488116 0.3011942 0.16529889 0.16529889 0.6703200 0.13533528 0.6703200
#>  [7,] 0.4493290 0.5488116 0.67032005 0.67032005 0.3678794 0.81873075 0.3678794
#>  [8,] 0.3011942 0.1652989 0.30119421 0.30119421 0.2465970 0.24659696 0.5488116
#>  [9,] 0.1652989 0.3011942 0.16529889 0.16529889 0.2018965 0.20189652 0.3011942
#> [10,] 0.1652989 0.3011942 0.16529889 0.16529889 0.2018965 0.20189652 0.3011942
#> [11,] 0.2018965 0.2465970 0.30119421 0.30119421 0.1652989 0.36787944 0.3678794
#> [12,] 0.5488116 0.6703200 0.24659696 0.24659696 0.4493290 0.44932896 0.6703200
#> [13,] 0.6703200 0.5488116 0.13533528 0.13533528 0.5488116 0.24659696 0.8187308
#> [14,] 0.5488116 0.6703200 0.24659696 0.24659696 0.4493290 0.44932896 0.6703200
#> [15,] 0.6703200 0.2465970 0.30119421 0.30119421 0.3678794 0.36787944 0.8187308
#> [16,] 0.5488116 0.3011942 0.54881164 0.54881164 0.3011942 0.67032005 0.6703200
#> [17,] 0.6703200 0.2465970 0.30119421 0.30119421 0.3678794 0.36787944 0.8187308
#> [18,] 0.3678794 0.6703200 0.36787944 0.36787944 0.4493290 0.44932896 0.3011942
#> [19,] 0.6703200 0.8187308 0.09071795 0.09071795 0.8187308 0.16529889 0.5488116
#> [20,] 0.4493290 0.5488116 0.67032005 0.67032005 0.3678794 0.81873075 0.3678794
#> [21,] 0.2465970 0.4493290 0.07427358 0.07427358 0.3011942 0.13533528 0.4493290
#> [22,] 0.3011942 0.5488116 0.30119421 0.30119421 0.3678794 0.36787944 0.3678794
#> [23,] 1.0000000 0.5488116 0.30119421 0.30119421 0.8187308 0.36787944 0.8187308
#> [24,] 0.3678794 0.1353353 0.16529889 0.16529889 0.2018965 0.20189652 0.6703200
#> [25,] 0.2465970 0.3011942 0.36787944 0.36787944 0.3011942 0.30119421 0.3011942
#> [26,] 0.5488116 0.6703200 0.24659696 0.24659696 0.6703200 0.30119421 0.6703200
#> [27,] 0.8187308 0.4493290 0.24659696 0.24659696 0.6703200 0.30119421 1.0000000
#> [28,] 0.6703200 0.2465970 0.30119421 0.30119421 0.5488116 0.24659696 0.8187308
#> [29,] 0.6703200 0.3678794 0.20189652 0.20189652 0.3678794 0.36787944 0.5488116
#> [30,] 0.3678794 0.4493290 0.54881164 0.54881164 0.3011942 0.67032005 0.4493290
#> [31,] 0.8187308 0.6703200 0.16529889 0.16529889 0.6703200 0.30119421 0.6703200
#> [32,] 0.8187308 0.6703200 0.54881164 0.54881164 0.6703200 0.67032005 0.6703200
#> [33,] 0.3011942 0.3678794 0.44932896 0.44932896 0.1652989 0.81873075 0.2465970
#> [34,] 0.5488116 0.4493290 0.36787944 0.36787944 0.3011942 0.67032005 0.4493290
#> [35,] 0.2465970 0.6703200 0.16529889 0.16529889 0.3011942 0.30119421 0.3011942
#> [36,] 0.3678794 0.3011942 0.81873075 0.81873075 0.2018965 1.00000000 0.3011942
#> [37,] 0.5488116 0.3011942 0.16529889 0.16529889 0.6703200 0.13533528 0.6703200
#> [38,] 0.1353353 0.3678794 0.09071795 0.09071795 0.1652989 0.16529889 0.2465970
#> [39,] 0.6703200 0.1652989 0.44932896 0.44932896 0.3678794 0.36787944 0.5488116
#> [40,] 0.3011942 0.1652989 0.09071795 0.09071795 0.3678794 0.07427358 0.5488116
#> [41,] 1.0000000 0.5488116 0.30119421 0.30119421 0.8187308 0.36787944 0.8187308
#> [42,] 0.5488116 1.0000000 0.16529889 0.16529889 0.6703200 0.30119421 0.4493290
#> [43,] 0.3011942 0.1652989 1.00000000 1.00000000 0.1652989 0.81873075 0.2465970
#> [44,] 0.3011942 0.1652989 1.00000000 1.00000000 0.1652989 0.81873075 0.2465970
#> [45,] 0.8187308 0.6703200 0.16529889 0.16529889 1.0000000 0.20189652 0.6703200
#> [46,] 0.3678794 0.3011942 0.81873075 0.81873075 0.2018965 1.00000000 0.3011942
#> [47,] 0.8187308 0.4493290 0.24659696 0.24659696 0.6703200 0.30119421 1.0000000
#> [48,] 0.3678794 0.1353353 0.16529889 0.16529889 0.3011942 0.13533528 0.6703200
#> [49,] 0.2465970 0.4493290 0.07427358 0.07427358 0.3011942 0.13533528 0.4493290
#> [50,] 0.6703200 0.5488116 0.13533528 0.13533528 0.8187308 0.16529889 0.8187308
#>            [,48]      [,49]     [,50]
#>  [1,] 0.13533528 0.30119421 0.1652989
#>  [2,] 0.24659696 0.54881164 0.4493290
#>  [3,] 0.36787944 0.16529889 0.6703200
#>  [4,] 0.16529889 0.36787944 0.6703200
#>  [5,] 0.16529889 0.07427358 0.1353353
#>  [6,] 0.67032005 0.30119421 0.8187308
#>  [7,] 0.16529889 0.24659696 0.3011942
#>  [8,] 0.81873075 0.36787944 0.4493290
#>  [9,] 0.30119421 0.67032005 0.3678794
#> [10,] 0.30119421 0.67032005 0.3678794
#> [11,] 0.36787944 0.54881164 0.3011942
#> [12,] 0.30119421 0.67032005 0.5488116
#> [13,] 0.36787944 0.54881164 0.6703200
#> [14,] 0.30119421 0.67032005 0.5488116
#> [15,] 0.54881164 0.24659696 0.4493290
#> [16,] 0.44932896 0.30119421 0.3678794
#> [17,] 0.54881164 0.24659696 0.4493290
#> [18,] 0.13533528 0.30119421 0.3678794
#> [19,] 0.16529889 0.36787944 0.6703200
#> [20,] 0.16529889 0.24659696 0.3011942
#> [21,] 0.30119421 1.00000000 0.5488116
#> [22,] 0.24659696 0.54881164 0.4493290
#> [23,] 0.36787944 0.24659696 0.6703200
#> [24,] 0.67032005 0.30119421 0.3678794
#> [25,] 0.30119421 0.30119421 0.3678794
#> [26,] 0.44932896 0.67032005 0.8187308
#> [27,] 0.67032005 0.44932896 0.8187308
#> [28,] 0.81873075 0.24659696 0.6703200
#> [29,] 0.16529889 0.16529889 0.3011942
#> [30,] 0.30119421 0.44932896 0.3678794
#> [31,] 0.20189652 0.30119421 0.5488116
#> [32,] 0.30119421 0.30119421 0.5488116
#> [33,] 0.07427358 0.16529889 0.1353353
#> [34,] 0.13533528 0.20189652 0.2465970
#> [35,] 0.13533528 0.67032005 0.3678794
#> [36,] 0.13533528 0.13533528 0.1652989
#> [37,] 0.67032005 0.30119421 0.8187308
#> [38,] 0.16529889 0.81873075 0.3011942
#> [39,] 0.36787944 0.07427358 0.3011942
#> [40,] 0.81873075 0.36787944 0.6703200
#> [41,] 0.36787944 0.24659696 0.6703200
#> [42,] 0.13533528 0.44932896 0.5488116
#> [43,] 0.16529889 0.07427358 0.1353353
#> [44,] 0.16529889 0.07427358 0.1353353
#> [45,] 0.30119421 0.30119421 0.8187308
#> [46,] 0.13533528 0.13533528 0.1652989
#> [47,] 0.67032005 0.44932896 0.8187308
#> [48,] 1.00000000 0.30119421 0.5488116
#> [49,] 0.30119421 1.00000000 0.5488116
#> [50,] 0.54881164 0.54881164 1.0000000
#> 
#> $f_hat
#>  [1] -0.275243274 -0.102664361 -0.012952182 -0.114753622  0.381098317
#>  [6]  0.483650452 -0.132220705 -0.146352921 -0.250107596 -0.250107596
#> [11] -0.436422405 -0.102715745  0.149961605 -0.102715745  0.168681966
#> [16] -0.012726562  0.168681966 -0.209024023 -0.114753622 -0.132220705
#> [21] -0.330048191 -0.102664361  0.136675073 -0.159160344  0.006849160
#> [26]  0.183990818  0.358902830  0.337033327  0.066027672 -0.125412416
#> [31]  0.069940056  0.029049223 -0.326926605 -0.153620490 -0.310082051
#> [36] -0.072654315  0.483650452 -0.457039912  0.185026556  0.639731957
#> [41]  0.136675073 -0.166134523  0.381098317  0.381098317  0.005106175
#> [46] -0.072654315  0.358902830  0.216317295 -0.330048191  0.423764982
#> 
#> $se
#> [1] 0.9889278
#> 
#> $h
#> [1] 5
#> 
#> $n
#> [1] 50
#> 
#> $method
#> [1] "RKHS regression (Gaussian kernel)"
#>