E(Y | X) = int X(t) beta(t) dt with beta given a series prior. Once X
is expanded on the same basis the model collapses to ridge regression
on the coefficient scores, which is exactly why a series prior is the
natural one here: the infinite-dimensional problem becomes a finite
penalised one with no approximation. Solved by Gauss-Seidel, the
normal equations being diagonally dominant after the unit ridge.
Usage
Ghosalfuncreg(n = 300, K = 4, seed = 42)
Arguments
- n
Sample size.
- K
Number of basis scores.
- seed
Seed for the deterministic draws.
Value
List with estimate (max absolute coefficient error),
beta_hat, method.
Details
Formula: beta_k <- sum_i (y_i - sum_{j != k} beta_j s_ij) s_ik
/ (sum_i s_ik^2 + 1).
References
Ghosal & van der Vaart (2017), Fundamentals of
Nonparametric Bayesian Inference, CUP, section 10.4.5.
Examples
Ghosalfuncreg()
#> $estimate
#> [1] 0.01831551
#>
#> $beta_hat
#> [1] 1.00759588 -0.51406630 0.24318589 0.01831551
#>
#> $method
#> [1] "functional regression (GvdV 2017 sec. 10.4.5)"
#>
#> attr(,"class")
#> [1] "morie_rich_result" "list"
