TRRsim {TRES} | R Documentation |
Generate simulation data for tensor response regression (TRR)
Description
This function is used to generate simulation data used in tensor response regression.
Usage
TRRsim(r, p, u, n)
Arguments
r |
The dimension of response, a vector with length larger than 2. |
p |
The dimension of predictor, a scale. |
u |
The structural dimension of envelopes at each mode, a vector with the same length as |
n |
The sample size. |
Details
The tensor response regression model is of the form,
where predictor , response
,
and the error term is tensor normal distributed as follows,
According to the tensor envelope structure, we have
for some ,
and
,
.
Value
x |
The predictor of dimension |
y |
The response of dimension |
Gamma |
The envelope subspace basis of dimension |
coefficients |
The tensor coefficients of dimension |
Sigma |
A lists of estimated covariance matrices at each mode for the error term, i.e., |
p , r , u |
The input |
Note
The length of r
must match that of u
, and each element of u
must be less than the corresponding element in r
.
References
Li, L. and Zhang, X., 2017. Parsimonious tensor response regression. Journal of the American Statistical Association, 112(519), pp.1131-1146.
See Also
Examples
r <- c(10, 10, 10)
u <- c(2, 2, 2)
p <- 5
n <- 100
dat <- TRRsim(r = r, p = p, u = u, n = n)
x <- dat$x
y <- dat$y
fit_std <- TRR.fit(x, y, method="standard")