slasso.fr {slasso}

Smooth LASSO estimator for the function-on-function linear regression model

Description

The smooth LASSO (S-LASSO) method for the function-on-function linear regression model provides interpretable coefficient function estimates that are both locally sparse and smooth (Centofanti et al., 2020).

Usage

slasso.fr(
  Y_fd,
  X_fd,
  basis_s,
  basis_t,
  lambda_L,
  lambda_s,
  lambda_t,
  B0 = 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.

lambda_L

Regularization parameter of the functional LASSO penalty.

lambda_s

Regularization parameter of the smoothness penalty along the s-direction.

lambda_t

Regularization parameter of the smoothness penalty along the t-direction.

B0

Initial estimator of the basis coefficients matrix of the coefficient function. Should have dimensions in accordance with the basis dimensions of basis_s and basis_t.

...

Other arguments to be passed to the Orthant-Wise Limited-memory Quasi-Newton optimization function. See the lbfgs help page of the package lbfgs.

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.

• lambdas_L: Regularization parameter of the functional LASSO penalty.

• lambda_s: Regularization parameter of the smoothness penalty along the s-direction.

• lambda_t: Regularization parameter of the smoothness penalty along the t-direction.

• Y_fd: The response functions.

• X_fd: The covariate functions.

• per_0: The fraction of domain where the coefficient function is zero.

• type: The output type.

References

Centofanti, F., Fontana, M., Lepore, A., & Vantini, S. (2020). Smooth LASSO Estimator for the Function-on-Function Linear Regression Model. arXiv preprint arXiv:2007.00529.

See Also

slasso.fr_cv

Examples

library(slasso)
data<-simulate_data("Scenario II",n_obs=150)
X_fd=data$X_fd
Y_fd=data$Y_fd
domain=c(0,1)
n_basis_s<-30
n_basis_t<-30
breaks_s<-seq(0,1,length.out = (n_basis_s-2))
breaks_t<-seq(0,1,length.out = (n_basis_t-2))
basis_s <- fda::create.bspline.basis(domain,breaks=breaks_s)
basis_t <- fda::create.bspline.basis(domain,breaks=breaks_t)
mod_slasso<-slasso.fr(Y_fd = Y_fd,X_fd=X_fd,basis_s=basis_s,basis_t=basis_t,
lambda_L = -1.5,lambda_s =-8,lambda_t = -7,B0 =NULL,invisible=1,max_iterations=10)