Y_i = f(x_i) + e_i with f = sum_{k <= K} beta_k phi_k. Choosing K by
the conjugate evidence rather than fixing it delivers the rate
n^(-2s/(2s+1)) without knowing s. The design is the equispaced
cosine basis, so the ridge fit is a per-coefficient shrinkage of the
empirical Fourier coefficient and no matrix has to be formed.
Usage
Ghosalfrsreg(n = 600, seed = 42)
Arguments
- n
Sample size.
- seed
Seed for the deterministic draws.
Value
List with estimate (integrated squared error against
the truth), K_hat, method.
Details
Formula: beta_k-hat = (n/(n+1)) mean_i y_i phi_k(x_i);
evidence(K) = -n log(RSS/n)/2 - K log(n)/2.
References
Ghosal & van der Vaart (2017), Fundamentals of
Nonparametric Bayesian Inference, CUP, section 10.4.2.
Examples
Ghosalfrsreg()
#> $estimate
#> [1] 0.003055023
#>
#> $K_hat
#> [1] 5
#>
#> $method
#> [1] "finite random series regression (GvdV 2017 sec. 10.4.2)"
#>
#> attr(,"class")
#> [1] "morie_rich_result" "list"
