CV_VARMLE {hdiVAR}

cross-validation for transition matrix update in maximization step

Description

Tune the tolerance parameter of generalized Dantzig selector and hard thresholding level via prediction error in test data.

Usage

CV_VARMLE(tol_seq, ht_seq, S0_train, S1_train, Y_test, is_echo = FALSE)

Arguments

tol_seq

vector; grid of tolerance parameter in Dantzig selector for cross-validation.

ht_seq

vector; grid of hard-thresholding levels for transition matrix estimate. To avoid hard thresholding, set ht_seq=0.

S0_train

a p by p matrix; average (over time points in training data) of conditional expectation of x_t x_t^\top on y_1, \ldots, y_T and parameter estimates, obtained from expectation step.

S1_train

a p by p matrix; average (over time points in training data) of conditional expectation of x_t x_{t+1}^\topon y_1, \ldots, y_T and parameter estimates, obtained from expectation step.

Y_test

a p by T_test matrix; observations of time series in test set.

is_echo

logical; if true, display the information of CV-optimal (tol, ht).

Value

a list of CV-optimal parameters and test prediction error.

tol_min	CV-optimal tolerance parameter in Dantzig selector.
ht_min	CV-optimal hard thresholding level for the output of Dantzig selector.
test_loss	a matrix of prediction error in test data; columns match tol_seq, and rows match ht_seq.

Author(s)

Xiang Lyu, Jian Kang, Lexin Li