nrrr.sim: Generate simulation data

In xliu-stat/NRRR: Multivariate Functional Regression via Nested Reduced-Rank Regularization

Description

This function generates simulation data for the nested reduced-rank regression under the multivariate functional regression scenario. With user-specified model dimensions and ranks, this function first generates functional multivariate predictors and responses and then transform the functional regression problem into a conventional finite-dimensional regression problem through basis expansion and truncation. The B-spline basis is used to conduct basis expansion.

Usage

NRRR.sim(n, ns, nt, r, rx, ry, jx, jy, p, d,
         s2n, rho_X, rho_E, Sigma = "CorrAR")

Arguments

n	sample size.
ns	number of time points at which the predictor trajectory is observed.
nt	number of time points at which the response trajectory is observed.
r	rank of the local reduced-rank structure.
rx	number of latent predictors.
ry	number of latent responses.
jx	number of basis functions to expand the predictor trajectory.
jy	number of basis functions to expand the response trajectory.
p	number of predictors.
d	number of responses.
s2n	a positive number to specify the signal to noise ratio.
rho_X	a scalar between 0 and 1 to specify the correlation strength among covariates.
rho_E	a scalar between 0 and 1 to specify the correlation strength among random errors.
Sigma	the correlation structure. Two options are available, "CorrAR": autoregressive, "CorrCS": compound symmetry.

Value

The function returns a list:

Ag	the matrix U.
Bg	the matrix V.
Al	the matrix A.
Bl	the matrix B.
C	the coefficient matrix C.
Alstar	A* in equation (7) of the NRRR paper.
Blstar	B* in equation (7) of the NRRR paper.
Cstar	(U \otimes I_jy)A* B*^T(V \otimes I_jx)^T in equation (7) of the NRRR paper.
tseq	a sequence of time points at which the response trajectory is observed.
psi	the set of basis functions to expand the response trajectory.
Jpsi	the correlation matrix of psi. Jpsihalf is (Jpsi)^(1/2).
sseq	a sequence of time points at which the predictor trajectory is observed.
phi	the set of basis functions to expand the predictor trajectory.
Jphi	the correlation matrix of phi.
E	the random error matrix.
Y	an array of dimension (n, d, nt), i.e., the generated response observations.
X	an array of dimension (n, p, ns), i.e., the generated predictor observations.
Ytrue	an array of dimension (n, d, nt). The response observations without random errors.
Yest	the response matrix used in NRRR estimation, and is of dimension n-by-jy*d.
Xest	the design matrix used in NRRR estimation, and is of dimension n-by-jx*p.

Examples

library(NRRR)
simDat <- NRRR.sim(n = 100, ns = 200, nt = 200, r = 5, rx = 3, ry = 3,
                   jx = 15, jy = 15, p = 10, d = 6, s2n = 1, rho_X = 0.5,
                   rho_E = 0, Sigma = "CorrAR")
simDat$Ag

xliu-stat/NRRR documentation built on Jan. 9, 2021, 3:23 p.m.