Cross-Validation for Bandwidth Selection

Implements least-squares cross-validation for bandwidth selection with any kernel function. Uses FFT-based algorithm for n >= 100 (fast, O(m log m) complexity) and exact computation for n < 100 (accurate). The FFT method bins data onto a regular grid and computes the LSCV objective via convolution in the frequency domain.

Usage

cv_bandwidth(
  X,
  h_grid = NULL,
  kernel_func,
  kernel_type = "normal",
  grid_size = 512
)

Arguments

X

A numerical vector of sample data.

h_grid

A numerical vector of bandwidth values to evaluate. If NULL (default), a grid is automatically generated based on the range and distribution of the data.

kernel_func

The kernel function to use for cross-validation.

kernel_type

A string identifying the kernel type, used only for reference bandwidth.

grid_size

Number of grid points for FFT-based evaluation (used when n >= 100). Default is 512. Larger values increase accuracy but reduce speed. Automatically rounded up to the next power of 2.

Value

A scalar representing the optimal bandwidth that minimizes the cross-validation score.

Examples

# Generate sample data
X <- rnorm(100)
# Get optimal bandwidth using cross-validation with a normal kernel
kernel_functions <- create_kernel_functions("normal")
h_opt <- cv_bandwidth(X, kernel_func = kernel_functions$kernel,
                     kernel_type = kernel_functions$kernel_type)