TPRsim {TRES} | R Documentation |
Generate simulation data for tensor predictor regression (TPR)
Description
This function is used to generate simulation data used in tensor prediction regression.
Usage
TPRsim(p, r, u, n)
Arguments
p |
The dimension of predictor, a vector in the form of |
r |
The dimension of response, a scale. |
u |
The structural dimension of envelopes at each mode, a vector with the same length as p. |
n |
The sample size. |
Details
The tensor predictor regression model is of the form,
where response , predictor
,
and the error term is multivariate normal distributed. The predictor is tensor normal distributed,
According to the tensor envelope structure, we have
for some ,
and
,
.
Value
x |
The predictor of dimension |
y |
The response of dimension |
Gamma |
A list of envelope subspace basis of dimension |
coefficients |
The tensor coefficients of dimension |
Sigma |
A lists of estimated covariance matrices at each mode for the tensor predictors, i.e., |
p , r , u |
The input |
Note
The length of p
must match that of u
, and each element of u
must be less than the corresponding element in p
.
References
Zhang, X. and Li, L., 2017. Tensor envelope partial least-squares regression. Technometrics, 59(4), pp.426-436.
See Also
Examples
p <- c(10, 10, 10)
u <- c(1, 1, 1)
r <- 5
n <- 200
dat <- TPRsim(p = p, r = r, u = u, n = n)
x <- dat$x
y <- dat$y
fit_std <- TPR.fit(x, y, method="standard")