estimate_ridge {CVEK} | R Documentation |
Estimating a Single Model
Description
Estimating projection matrices and parameter estimates for a single model.
Usage
estimate_ridge(
Y,
X,
K,
lambda,
compute_kernel_terms = TRUE,
converge_thres = 1e-04
)
Arguments
Y |
(matrix, n*1) The vector of response variable. |
X |
(matrix, n*d_fix) The fixed effect matrix. |
K |
(list of matrices) A nested list of kernel term matrices, corresponding to each kernel term specified in the formula for a base kernel function in kern_func_list. |
lambda |
(numeric) A numeric string specifying the range of tuning parameter to be chosen. The lower limit of lambda must be above 0. |
compute_kernel_terms |
(logic) Whether to computing effect for each individual terms. If FALSE then only compute the overall effect. |
converge_thres |
(numeric) The convergence threshold for computing kernel terms. |
Details
For a single model, we can calculate the output of gaussian process regression, the solution is given by
\hat{\beta}=[X^T(K+\lambda
I)^{-1}X]^{-1}X^T(K+\lambda I)^{-1}y
\hat{\alpha}=(K+\lambda
I)^{-1}(y-\hat{\beta}X)
.
Value
beta |
(matrix, d_fixed*1) Fixed effect estimates. |
alpha |
(matrix, n*k_terms) Kernel effect estimates for each kernel term. |
kern_term_mat |
(matrix, n*k_terms) Kernel effect for each kernel term. |
A_list |
(list of length k_terms) Projection matrices for each kernel term. |
proj_matrix |
(list of length 4) Estimated projection matrices, combined across kernel terms. |
Author(s)
Wenying Deng
References
Andreas Buja, Trevor Hastie, and Robert Tibshirani. (1989) Linear Smoothers and Additive Models. Ann. Statist. Volume 17, Number 2, 453-510.