rrs.fit {rrpack}

Fitting reduced-rank ridge regression with given rank and shrinkage penalty

Description

Fitting reduced-rank ridge regression with given rank and shrinkage penalty

Usage

rrs.fit(Y, X, nrank = min(ncol(Y), ncol(X)), lambda = 1, coefSVD = FALSE)

Arguments

Y

a matrix of response (n by q)

X

a matrix of covariate (n by p)

nrank

an integer specifying the desired rank

lambda

tunging parameter for the ridge penalty

coefSVD

logical indicating the need for SVD for the coeffient matrix int the output

Value

S3 rrr object, a list consisting of

coef

coefficient of rrs

coef.ls

coefficient of least square

fitted

fitted value of rrs

fitted.ls

fitted value of least square

A

right singular matrix

Ad

sigular value vector

nrank

rank of the fitted rrr

References

Mukherjee, A. and Zhu, J. (2011) Reduced rank ridge regression and its kernal extensions.

Mukherjee, A., Chen, K., Wang, N. and Zhu, J. (2015) On the degrees of freedom of reduced-rank estimators in multivariate regression. Biometrika, 102, 457–477.

Examples

library(rrpack)
Y <- matrix(rnorm(400), 100, 4)
X <- matrix(rnorm(800), 100, 8)
rfit <- rrs.fit(Y, X)