adass.fr {adass}

Adaptive smoothing spline estimator for the function-on-function linear regression model

Description

The adaptive smoothing spline (AdaSS) estimator for the function-on-function linear regression proposed in Centofanti et al., 2020.

Usage

adass.fr(
  Y_fd,
  X_fd,
  basis_s,
  basis_t,
  beta_ders = NULL,
  beta_dert = NULL,
  grid_eval_ders = NULL,
  grid_eval_dert = NULL,
  tun_par = c(lambda_s = 10^4, lambda_t = 10^4, delta_s = 0, gamma_s = 1, delta_t = 0,
    delta_t = 1),
  CV = FALSE,
  K = 10,
  X_fd_test = NULL,
  Y_fd_test = NULL
)

Arguments

Y_fd

An object of class fd corresponding to the response functions.

X_fd

An object of class fd corresponding to the covariate functions.

basis_s

B-splines basis along the s-direction of class basisfd.

basis_t

B-splines basis along the t-direction of class basisfd.

beta_ders

Initial estimate of the partial derivative of the coefficient function along the s-direction. Either a matrix or a class basisfd object. If NULL no adaptive penalty is used along the s-direction.

beta_dert

Initial estimate of the partial derivative of the coefficient function along the t-direction. Either a matrix or a class basisfd object. If NULL no adaptive penalty is used along the t-direction.

grid_eval_ders

Grid of evaluation of the partial derivatives along the s-direction.

grid_eval_dert

Grid of evaluation of the partial derivatives along the t-direction.

tun_par

Vector of tuning parameters.

CV

If TRUE the K-fold cross-validation prediction error is calculated. Default is FALSE. If X_fd_test and Y_fd_test are both provided the prediction error on the test set is calculated in place of the cross-validation prediction error when CV is TRUE.

K

Number of folds. Default is 10.

X_fd_test

Test set covariate functions. Default is NULL.

Y_fd_test

Test set response functions. Default is NULL.

Value

A list containing the following arguments:

• B: The basis coefficients matrix estimate of the coefficient function.

• Beta_hat_fd: The coefficient function estimate of class bifd.

• alpha: The intercept function estimate.

• tun_par: Vector of tuning parameters.

• CV: Estimated prediction error.

• CV_sd: Standard error of the estimated prediction error.

• Y_fd: The response functions.

• X_fd: The covariate functions.

References

Centofanti, F., Lepore, A., Menafoglio, A., Palumbo, B., Vantini, S. (2023). Adaptive Smoothing Spline Estimator for the Function-on-Function Linear Regression Model. Computational Statistics 38(1), 191–216.

See Also

adass.fr_eaass

Examples

library(adass)
data<-simulate_data("Scenario HAT",n_obs=100)
X_fd=data$X_fd
Y_fd=data$Y_fd
basis_s <- fda::create.bspline.basis(c(0,1),nbasis = 10,norder = 4)
basis_t <- fda::create.bspline.basis(c(0,1),nbasis = 10,norder = 4)
mod_smooth <-adass.fr(Y_fd,X_fd,basis_s = basis_s,basis_t = basis_t,tun_par=c(10^-6,10^-6,0,0,0,0))
grid_s<-seq(0,1,length.out = 10)
grid_t<-seq(0,1,length.out = 10)
beta_der_eval_s<-fda::eval.bifd(grid_s,grid_t,mod_smooth$Beta_hat_fd,sLfdobj = 2)
beta_der_eval_t<-fda::eval.bifd(grid_s,grid_t,mod_smooth$Beta_hat_fd,tLfdobj = 2)
mod_adass <-adass.fr(Y_fd, X_fd, basis_s = basis_s, basis_t = basis_t,
                     tun_par=c(10^-6,10^-6,0,1,0,1),beta_ders = beta_der_eval_s,
                     beta_dert = beta_der_eval_t,grid_eval_ders=grid_s,grid_eval_dert=grid_t )