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Renvlp (version 2.7)

stenvMU: Estimate the simultaneous envelope subspace

Description

Estimate the simulatneous envelope subspace with specified dimension.

Usage

stenvMU(X, Y, q, u)

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.

q

Dimension of the X-envelope. An integer between 0 and p.

u

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

Value

Gammahat

The orthonormal basis of the Y-envelope subspace.

Gamma0hat

The orthonormal basis of the complement of the Y-envelope subspace.

Phihat

The orthonormal basis of the X-envelope subspace.

Phi0hat

The orthonormal basis of the complement of the X-envelope subspace.

objfun

The minimized objective function.

Details

This function estimate the simultaneous envelope subspace using an non-Grassmann optimization algorithm.

References

Cook, R. D., Forzani, L. and Su, Z. (2016) A Note on Fast Envelope Estimation. Journal of Multivariate Analysis. 150, 42-54.