TensEnv_dim

A vector predictor of dimension p.

The response tensor instance \(r_1\times \cdots \times r_m\).

The parameter in <code>ballGBB1D_bic</code>.

multiD

The maximum envelope dimension to be considered, the parameter in <code>ballGBB1D_bic</code>.

bic_max

opts

This function use the 1D-BIC criterion by by Zhang, X., &amp; Mai, Q. (2018) to select envelope dimensions in tensor response regression.

Provides three estimators for tensor response regression (TRR) and tensor predictor regression (TPR) models with tensor envelope structure. The three types of estimation approaches are generic and can be applied to any envelope estimation problems. The full Grassmannian (FG) optimization is often associated with likelihood-based estimation but requires heavy computation and good initialization; the one-directional optimization approaches (1D and ECD algorithms) are faster, stable and does not require carefully chosen initial values; the SIMPLS-type is motivated by the partial least squares regression and is computationally the least expensive.

TensEnv_dim: Envelope dimension selection for tensor response regression

Description

Usage

Arguments

Value