Renvlp (version 3.4)

cv.env.tcond: Cross validation for env.tcond

Description

Compute the prediction error using m-fold cross validation for the response envelope estimator where the errors follow a t-distribution.

Usage

cv.env.tcond(X, Y, u, df, 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.

df

Degrees of freedom of the t-distribution. A positive number that is greater than 2.

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(concrete)
X <- concrete[1:78, 1:7]  # The first 78 observations are training data
Y <- concrete[1:78, 8:10]
if (FALSE) u <- u.env.tcond(X, Y, 6)
if (FALSE) u

m <- 5
nperm <- 50
if (FALSE) cvPE <- cv.env.tcond(X, Y, 2, 6, m, nperm)
if (FALSE) cvPE