Renvlp (version 3.4.5)

cv.rrenv: Cross validation for rrenv

Description

Compute the prediction error using m-fold cross validation for the reduced rank envelope estimator.

Usage

cv.rrenv(X, Y, u, d, m, nperm)

Value

The output is a real nonnegative number.

cvPE

The prediction error estimated by m-fold cross validation.

Arguments

X

Predictors. An n by p matrix, p is the number of predictors. The predictors can be univariate or multivariate, discrete or continuous.

Y

Multivariate responses. An n by r matrix, r is the number of responses and n is number of observations. The responses must be continuous variables.

u

Dimension of the envelope. An integer between 0 and r.

d

The rank of the coefficient matrix. An integer between 0 and u.

m

A positive integer that is used to indicate m-fold cross validation.

nperm

A positive integer indicating number of permutations of the observations, m-fold cross validation is run on each permutation.

Details

This function computes prediction errors using m-fold cross validation. For a fixed dimension u, the data is randomly partitioned into m parts, each part is in turn used for testing for the prediction performance while the rest m-1 parts are used for training. This process is repeated for nperm times, and average prediction error is reported. As Y is multivariate, the identity inner product is used for computing the prediction errors.

Examples

data(vehicles)
X <- vehicles[, 1:11]  
Y <- vehicles[, 12:15]
X <- scale(X)
Y <- scale(Y)  # The scales of Y are vastly different, so scaling is reasonable here

m <- 5
nperm <- 50
if (FALSE) cvPE <- cv.rrenv(X, Y, 4, 2, m, nperm)
if (FALSE) cvPE