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TRES (version 1.1.3)

TPRsim: 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 (p1,,pm).

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.

Value

x

The predictor of dimension p1××pm×n.

y

The response of dimension r×n.

Gamma

A list of envelope subspace basis of dimension pk×uk, k=1,,m.

coefficients

The tensor coefficients of dimension p1××pm×r.

Sigma

A lists of estimated covariance matrices at each mode for the tensor predictors, i.e., Σ1,,Σm.

p, r, u

The input p,r,u.

Details

The tensor predictor regression model is of the form, Y=B(m+1)vec(X)+ϵ where response YRr, predictor XRp1××pm, B∈∈Rp1××pm×r and the error term is multivariate normal distributed. The predictor is tensor normal distributed, XTN(0;Σ1,,Σm) According to the tensor envelope structure, we have B=[Θ;Γ1,,Γm,Ip], Σk=ΓkΩkΓkT+Γ0kΩ0kΓ0kT, for some ΘRu1××um×p, ΩkRuk×uk and Ω0k∈∈R(pkuk)×(pkuk), k=1,,m.

References

Zhang, X. and Li, L., 2017. Tensor envelope partial least-squares regression. Technometrics, 59(4), pp.426-436.

See Also

TPR.fit, TRRsim.

Examples

Run this code
# NOT RUN {
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")

# }

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