itdr (version 2.0.1)

mitdr: Integral Transformation Methods for SDR Subspaces in Multivariate Regression

Description

The ``mitdr()'' function implements transformation method for multivariate regression

Usage

mitdr(X,Y,d,m,method="FT-IRE",
                lambda=NA,noB = 5,noC = 20,noW = 2,sparse.cov = FALSE, x.scale = FALSE)

Value

The function output is a p-by-d matrix and the estimated covariance matrix.

Beta_hat

An estimator for the SDR subspace.

sigma_X

Estimated covariance matrix only from the ``admmft'' method and a null matrix for other methods.

Arguments

X

Design matrix with dimension n-by-p

Y

Response matrix with dimension n-by-q

d

Structure dimension (default 2).

m

The number of omegas, i.e., 2m number of integral transforms

method

(default ``FT-IRE'') Specify the method of dimension reduction. Other possible choices are ``FT-DIRE'',``FT-SIRE'',``FT-RIRE'', ``FT-DRIRE'', and ``admmft''.

lambda

Tuning Parameter for ``admmft'' method. If it is not provided, the optimal lambda value is chosen by cross-validation of the Fourier transformation method.

noB

(default 5) Iterations for updating B. Only required for the ``admmft'' method.

noC

(default 20) Iterations for updating C. Only required for the ``admmft'' method.

noW

(default 2) Iterations for updating weight. Only required for the ``admmft'' method.

sparse.cov

(default FALSE) If TRUE, calculates the soft-threshold matrix. Only required for the ``admmft'' method.

x.scale

(default FALSE) If TRUE, standardizes each variable for the soft-threshold matrix. Only required for the ``admmft'' method.

Details

The ``mitdr()'' function selects the sufficient variables using Fourier transformation sparse inverse regression estimators.

References

Weng, J. (2022), Fourier Transform Sparse Inverse Regression Estimators for Sufficient Variable Selection, Computational Statistics & Data Analysis, 168, 107380.

Weng, J., & Yin, X. (2022). A Minimum Discrepancy Approach with Fourier Transform in Sufficient Dimension Reduction. Statistica Sinica, 32.

Examples

if (FALSE) {
data(prostate)
Y <- as.matrix(prostate[, 9])
X <- as.matrix(prostate[, -9])
fit.ftire <- mitdr(X, Y, d = 1, method = "FT-DRIRE")
fit.ftire$Beta_hat
}