Estimate the scaled envelope subspace in the predictor space with specified dimension.
sxenvMU(X, Y, u, R, initial = NULL)Predictors. An n by p matrix, p is the number of predictors. The predictors can be univariate or multivariate, discrete or continuous.
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.
Dimension of the scaled envelope in the predictor space. An integer between 0 and p.
The number of replications of the scales. A vector, the sum of all elements of R must be p.
The user-specified value of Gamma for the envelope subspace.
The orthonormal basis of the scaled envelope subspace in the predictor space.
The orthonormal basis of the complement of the scaled envelope subspace in the predictor space.
The matrix of estimated scales.
The minimized objective function.
This function estimate the scaled envelope subspace in the predictor space using an non-Grassmann optimization algorithm and nonlinear optimization using augmented Lagrange method.
Cook, R. D., Forzani, L. and Su, Z. (2016) A Note on Fast Envelope Estimation. Journal of Multivariate Analysis. 150, 42-54.
Ye, Y., Interior algorithms for linear, quadratic, and linearly constrained non linear programming, PhD Thesis, Departments of EES stanford University, Stanford CA.