mitdr {itdr}

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)

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.

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.

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

## Not run: 
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

## End(Not run)