TRES (version 0.1.0)

TRR: Tensor response regression

Description

This function is used for estimation of tensor response regression. The avaiable method including standard OLS type estimation, PLS type of estimation as well as envelope estimation with 1D and ECD approaches.

Usage

TRR(Yn, Xn, u, method)

Arguments

Yn

The response tensor instance or dimension \(r_1\times r_2\times\cdots\times r_m \times n\), where \(n\) is the sample size.

Xn

The predictor matrix of dimension \(p \times n\).

u

The dimension of envelope subspace. \(u=(u_1,\cdots, u_m)\).

method

The method used for estimation of tensor response regression. There are four possible choices.

Value

Bhat

The estimation of regression coefficient tensor.

Gamma_hat

The estimation of envelope subspace basis.

Sig

A matrix lists of \(\boldsymbol{\Sigma}_k\), where \(\boldsymbol{\Sigma}=\boldsymbol{\Sigma}_m \otimes \cdots \otimes \boldsymbol{\Sigma}_1\).

Examples

# NOT RUN {
rm(list=ls())

r <- c(10, 10, 10)
m <- length(r)
u <- c(2, 2, 2)
p <- 5
n <- 100


set.seed(1)
eta <- array(runif(prod(u)*p), c(u, p))
eta <- as.tensor(eta)

Gamma <- Gamma0 <- Omega <- Omega0 <- Sig <- Sigsqrtm <- NULL
for (i in 1:m){
  tmp <- matrix(runif(r[i]*u[i]), r[i], u[i])
  Gamma[[i]] <- qr.Q(qr(tmp))
  Gamma0[[i]] <- qr.Q(qr(Gamma[[i]]),complete=TRUE)[,(u[i]+1):r[i]]

  A <- matrix(runif(u[i]^2), u[i], u[i])
  Omega[[i]] <- A %*% t(A)
  A <- matrix(runif((r[i]-u[i])^2), (r[i]-u[i]), (r[i]-u[i]))
  Omega0[[i]] <- A %*% t(A)
  Sig[[i]] <- Gamma[[i]] %*% Omega[[i]] %*% t(Gamma[[i]])+
    Gamma0[[i]] %*% Omega0[[i]] %*% t(Gamma0[[i]])
  Sig[[i]] <- 10*Sig[[i]]/norm(Sig[[i]], type="F")+0.01*diag(r[i])
  Sigsqrtm[[i]] <- pracma::sqrtm(Sig[[i]])$B
}
B <- ttl(eta, Gamma, ms=1:m)
Xn <- matrix(rnorm(p*n), p, n)
Xn_inv <- MASS::ginv(Xn %*% t(Xn)) %*% Xn
Epsilon <- array(rnorm(prod(r)*n), c(r, n))
Epsilon <- as.tensor(Epsilon)
Epsilon <- ttl(Epsilon, Sigsqrtm, ms=1:m)
Yn <- Epsilon + ttm(B, t(Xn), m+1)

res_ECD = TRR(Yn, Xn, u, method="ECD")
res_1D = TRR(Yn, Xn, u, method="1D")
res_pls = TRR(Yn, Xn, u, method="PLS")
res_std = TRR(Yn, Xn, u, method="standard")

rTensor::fnorm(B-res_ECD$Bhat)
rTensor::fnorm(B-res_1D$Bhat)
rTensor::fnorm(B-res_pls$Bhat)
rTensor::fnorm(B-res_std$Bhat)
# }