predict_fof_pc function

Use a function-on-function linear regression model for prediction

Predict new observations of the functional response variable and calculate the corresponding prediction error (and their standardized or studentized version) given new observations of functional covariates and a fitted function-on-function linear regression model.

predict_fof_pc(object, mfdobj_y_new, mfdobj_x_new)

Arguments

• object: A list obtained as output from fof_pc, i.e. a fitted function-on-function linear regression model.
• mfdobj_y_new: An object of class mfd containing new observations of the functional response.
• mfdobj_x_new: An object of class mfd containing new observations of the functional covariates.

Returns

A list of mfd objects. It contains:

• pred_error: the prediction error of the standardized functional response variable,
• pred_error_original_scale: the prediction error of the functional response variable on the original scale,
• y_hat_new: the prediction of the functional response observations on the original scale,
• y_z_new: the standardized version of the functional response observations provided in mfdobj_y_new,
• y_hat_z_new: the prediction of the functional response observations on the standardized/studentized scale.

Examples

library(funcharts)
data("air")
air <- lapply(air, function(x) x[1:10, , drop = FALSE])
fun_covariates <- c("CO", "temperature")
mfdobj_x <- get_mfd_list(air[fun_covariates], lambda = 1e-2)
mfdobj_y <- get_mfd_list(air["NO2"], lambda = 1e-2)
mod <- fof_pc(mfdobj_y, mfdobj_x)
predict_fof_pc(mod,
               mfdobj_y_new = mfdobj_y,
               mfdobj_x_new = mfdobj_x)

References

Centofanti F, Lepore A, Menafoglio A, Palumbo B, Vantini S. (2021) Functional Regression Control Chart. Technometrics, 63(3):281--294. doi:10.1080/00401706.2020.1753581

Author(s)

C. Capezza, F. Centofanti