Renvlp (version 3.4.5)

pred.felmKL: Estimation or prediction for felmKL

Description

Perform estimation or prediction under the functional envelope linear model, using Karhunen-Loeve expansion based estimation.

Usage

pred.felmKL(X, Y, ux, uy, t1, t2, Xnew, knots = c(0, 0.25, 0.5, 0.75, 1))

Value

The output is a list that contains following components.

value

The fitted value or the predicted value evaluated at Xnew. The fitted or predicted values are at the same observation points as Y.

covMatrix.estm

The covariance matrix of the fitted value at Xnew.

SE.estm

The standard error of the fitted value at Xnew.

covMatrix.pred

The covariance matrix of the predicted value at Xnew.

SE.pred

The standard error of the predicted value at Xnew.

Arguments

X

Predictor function. An n by T1 matrix, T1 is number of observed time points, which is the length of t1. Here we assume that each function is observed at the same time points.

Y

Response function. An n by T2 matrix, T2 is number of observed time points, which is the length of t2. Here we assume that each function is observed at the same time points.

ux

Dimension of the predictor envelope. An integer between 0 and number of knots +2.

uy

Dimension of the response envelope. An integer between 0 and number of knots +2.

t1

The observed time points for the predictor functions.

t2

The observed time points for the response functions.

Xnew

The value of X with which to estimate or predict Y. A T1 dimensional vector. The observed time points should be the same as those of X.

knots

The location of knots of the cubic splines used for estimation. Locations should be positive. The default location of the knots are 0, 0.25, 0.5, 0.75, 1.

Details

This function evaluates the functional envelope linear model at new value Xnew. It can perform estimation: find the fitted value when X = Xnew, or prediction: predict Y when X = Xnew. The covariance matrix and the standard errors are also provided. The estimation method uses the Karhunen-Loeve expansion based estimation in Su et al. (2022) with cubic splines.

References

Su, Z., Li, B. and Cook, R. D. (2022+) Envelope model for function-on-function linear regression.

Examples

data(NJdata)
dataX <- matrix(NJdata[,6], nrow = 21)
X <- as.matrix(dataX[, 32:61])
dataY <- matrix(NJdata[,3], nrow = 21)
Y <- as.matrix(dataY[, 32:61])
t1 <- 0:29
t2 <- t1

m <- pred.felmKL(X, Y, 4, 3, t1, t2, X[1,])
m$value
m$SE.estm
m$SE.pred