TRES (version 1.1.1)

TensPLS_cv2d3d: Envelope dimension by cross-validation for tensor predictor regression (TPR).

Description

Select the envelope dimension by cross-validation for tensor predictor regression.

Usage

TensPLS_cv2d3d(x, y, maxdim=10, nfolds=5)

Arguments

x

The predictor tensor instance of dimension \(p_1\times p_2\times\cdots\times p_m \times n\), where \(n\) is the sample size. Array with the same dimensions and matrix with dimension \(p\times n\) are acceptable.

y

The response matrix of dimension \(r \times n\), where \(n\) is the sample size. Vector of length \(n\) is acceptable.

maxdim

The largest dimension to be considered for selection.

nfolds

Number of folds for cross-validation.

Value

mincv

The minimum sum of squared error.

u

The envelope subspace dimension selected.

References

Zhang, X., & Li, L. (2017). Tensor Envelope Partial Least-Squares Regression. Technometrics, 59(4), 426-436.

See Also

TPR_sim.

Examples

# NOT RUN {
rm(list = ls())
# The dimension of predictor
p <- c(10, 10, 10)
# The envelope dimensions u.
u <- c(1, 1, 1)
# The dimension of response
r <- 5
# The sample size
n <- 200

dat <- TPR_sim(p = p, r = r, u = u, n = n)
x <- dat$x
y <- dat$y

## It is time-consuming
# }
# NOT RUN {
  TensPLS_cv2d3d(x, y, maxdim = 5) # The estimated envelope dimensions are the same as u.
# }
# NOT RUN {
## Use dataset square, but it is time-consuming
# }
# NOT RUN {
  data("square")
  x <- square$x
  y <- square$y
  # check the dimension of x
  dim(x)
  # use 32 as the maximal envelope dimension
  TensPLS_cv2d3d(x, y, maxdim=32)
# }