predict_ff_regression function

Prediction for a function-on-function regression model

This function is used to make prediction for a new set of functional predictors based upon a fitted function-on-function regression model in the output of rob.ff.reg.

predict_ff_regression(object, Xnew)

Arguments

• object: An output object obtained from rob.ff.reg.
• Xnew: A list of matrices consisting of the new observations of functional predictors. The argument Xnew must have the same length and the same structure as the input X of rob.ff.reg.

Returns

An $n_{test} \times p$-dimensional matrix of predicted functions of the response variable for the given set of new functional predictors Xnew. Here, $n_{test}$, the number of rows of the matrix of predicted values, equals to the number of rows of Xnew, and $p$ equals to the number of columns of Y, the input in the rob.ff.reg.

Author(s)

Ufuk Beyaztas and Han Lin Shang

Examples

set.seed(2022)
sim.data <- generate.ff.data(n.pred = 5, n.curve = 200, n.gp = 101, out.p = 0.1)
out.indx <- sim.data$out.indx
Y <- sim.data$Y
X <- sim.data$X
indx.test <- sample(c(1:200)[-out.indx], 60)
indx.train <- c(1:200)[-indx.test]
Y.train <- Y[indx.train,]
Y.test <- Y[indx.test,]
X.train <- X.test <- list()
for(i in 1:5){
  X.train[[i]] <- X[[i]][indx.train,]
  X.test[[i]] <- X[[i]][indx.test,]
}
gpY = seq(0, 1, length.out = 101) # grid points of Y
gpX <- rep(list(seq(0, 1, length.out = 101)), 5) # grid points of Xs

model.MM <- rob.ff.reg(Y = Y.train, X = X.train, model = "full", emodel = "robust",
                       fmodel = "MM", gpY = gpY, gpX = gpX)
pred.MM <- predict_ff_regression(object = model.MM, Xnew = X.test)
round(mean((Y.test - pred.MM)^2), 4)        # 0.5925 (MM method)