estimate_base: Estimating Projection Matrices

In CVEK: Cross-Validated Kernel Ensemble

Description

Calculate the estimated projection matrices for every kernels in the kernel library.

Usage

estimate_base(Y, X, K_list, mode, lambda, ...)

Arguments

Y	(matrix, n*1) The vector of response variable.
X	(matrix, n*d_fix) The fixed effect matrix.
K_list	(list of matrices) A nested list of kernel term matrices. The first level corresponds to each base kernel function in kern_func_list, the second level corresponds to each kernel term specified in the formula.
mode	(character) A character string indicating which tuning parameter criteria is to be used.
lambda	(numeric) A numeric string specifying the range of tuning parameter to be chosen. The lower limit of lambda must be above 0.
...	Additional parameters to pass to estimate_ridge.

Details

For a given mode, this function returns a list of projection matrices for every kernel in the kernel library and a n*K matrix indicating errors.

Value

A_hat	(list of length K) A list of projection matrices for each kernel in the kernel library.
P_K_hat	(list of length K) A list of projection matrices to kernel space for each kernel in the kernel library.
beta_list	(list of length K) A list of fixed effect estimators for each kernel in the kernel library.
alpha_list	(list of length K) A list of kernel effect estimates for each kernel in the kernel library.
kern_term_list	(list of length K) A list of kernel effects for each kernel in the kernel library.
A_proc_list	(list of length K) A list of projection matrices for each kernel in the kernel library.
lambda_list	(list of length K) A list of selected tuning parameters for each kernel in the kernel library.
error_mat	(matrix, n*K) A n\*K matrix indicating errors.

Author(s)

Wenying Deng

References

Jeremiah Zhe Liu and Brent Coull. Robust Hypothesis Test for Nonlinear Effect with Gaussian Processes. October 2017.

CVEK documentation built on Jan. 8, 2021, 5:42 p.m.