select_wavelet: Cross-validated choice of (j0, h) for the wavelet estimator

In qdfauction: Nonparametric Quantile Density Estimation and Structural Analysis of First-Price Auctions

Cross-validated choice of (j0, h) for the wavelet estimator

Description

Chooses the resolution level and the post-smoothing bandwidth of [qdf_wavelet()] by 'folds'-fold cross-validation. The implied density of the data is \hat g(x) = 1/\hat q(\hat G_{\rm train}(x)). With 'criterion = "lscv"' (default) the pair minimises the least-squares criterion \int \hat g^2 - 2 n_k^{-1} \sum \hat g(x_i) over held-out observations, using \int \hat g(x)^2 dx = \int_0^1 1/\hat q(u)\,du; this targets integrated squared error (Rudemo 1982; Bowman 1984). With 'criterion = "loglik"' it maximises the held-out log-likelihood. Pairs with h below the lattice spacing 1/(2^{j_0}-1) are not considered, since the local-linear smoother is then ill-conditioned.

Usage

select_wavelet(
  x,
  j0_grid = 3:6,
  h_grid = c(0.03, 0.05, 0.08, 0.12, 0.2, 0.3),
  folds = 5L,
  criterion = c("lscv", "loglik"),
  ...
)

Arguments

x	numeric sample.
j0_grid, h_grid	candidate values.
folds	number of folds.
criterion	'"lscv"' or '"loglik"'.
...	passed to [qdf_wavelet()] (e.g. 'threshold', 'smooth', 'filter').

Value

a list with 'j0', 'h', and the matrix of criterion values ('ll', rows 'j0_grid', columns 'h_grid').

Reproducibility

Fold assignment (or bootstrap resampling) uses R's random number generator; call [set.seed()] beforehand to make results exactly reproducible.

Examples

set.seed(2)
x <- rbeta(300, 0.5, 0.5)
select_wavelet(x, j0_grid = 4:6, h_grid = c(0.05, 0.15), folds = 3)

qdfauction documentation built on Nov. 10, 2026, 5:07 p.m.