With p(x) = Psi(W_x) and W an s-smooth Gaussian process on the unit
cube in d dimensions, the concentration function grows like
eps^(-d/s); feeding that exponent into the rate equation of Theorem
11.20 gives eps_n = n^(-s/(2s+d)). The binary-regression case adds
nothing new to the machinery – that is the point of Theorem 11.22.
Usage
Ghosalgpbinregcrt(s = 2, d = 1, ns = c(100, 10000))
Arguments
- s
Smoothness of the process.
- d
Dimension of the covariate.
- ns
Vector of sample sizes.
Value
List with estimate (rate at the largest n),
rate_by_n, exponent, method.
Details
Formula: eps_n = n^(-s/(2s+d)).
References
Ghosal & van der Vaart (2017), Fundamentals of
Nonparametric Bayesian Inference, CUP, Theorems 11.20 and 11.22.
Examples
Ghosalgpbinregcrt()
#> $estimate
#> [1] 0.02511886
#>
#> $rate_by_n
#> [1] 0.15848932 0.02511886
#>
#> $exponent
#> [1] 0.4
#>
#> $method
#> [1] "GP binary regression rate (GvdV 2017 Thm 11.22)"
#>
#> attr(,"class")
#> [1] "morie_rich_result" "list"
