Adaptive Smoothing Spline Estimator for the Function-on-Function Linear Regression Model

11/24/2020
by   Fabio Centofanti, et al.
0

In this paper, we propose an adaptive smoothing spline (AdaSS) estimator for the function-on-function linear regression model where each value of the response, at any domain point, depends on the full trajectory of the predictor. The AdaSS estimator is obtained by the optimization of an objective function with two spatially adaptive penalties, based on initial estimates of the partial derivatives of the regression coefficient function. This allows the proposed estimator to adapt more easily to the true coefficient function over regions of large curvature and not to be undersmoothed over the remaining part of the domain. A novel evolutionary algorithm is developed ad hoc to obtain the optimization tuning parameters. Extensive Monte Carlo simulations have been carried out to compare the AdaSS estimator with competitors that have already appeared in the literature before. The results show that our proposal mostly outperforms the competitor in terms of estimation and prediction accuracy. Lastly, those advantages are illustrated also on two real-data benchmark examples.

READ FULL TEXT

Authors

page 1

page 2

page 3

page 4

07/01/2020

Smooth Lasso Estimator for the Function-on-Function Linear Regression Model

A new estimator, named as S-LASSO, is proposed for the coefficient funct...
08/03/2019

On estimation and prediction in spatial functional linear regression model

We consider a spatial functional linear regression, where a scalar respo...
09/28/2021

Statistical inference for function-on-function linear regression

Function-on-function linear regression is important for understanding th...
09/27/2021

Locally Sparse Function on function Regression

In functional data analysis, functional linear regression has attracted ...
11/15/2020

Semiparametric inference for the scale-mixture of normal partial linear regression model with censored data

In the framework of censored data modeling, the classical linear regress...
08/14/2019

Least Squares Approximation for a Distributed System

In this work we develop a distributed least squares approximation (DLSA)...
09/16/2020

An Intrinsic Treatment of Stochastic Linear Regression

Linear regression is perhaps one of the most popular statistical concept...
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.