Partially linear varying coefficient models stratified by a functional covariate

Abstract

We consider the problem of estimation in semiparametric varying coefficient models where the covariate modifying the varying coefficients is functional and is modeled nonparametrically. We develop a kernel-based estimator of the nonparametric component and a profiling estimator of the parametric component of the model and derive their asymptotic properties. Specifically, we show the consistency of the nonparametric functional estimates and derive the asymptotic expansion of the estimates of the parametric component. We illustrate the performance of our methodology using a simulation study and a real data application.

Error variance estimation in semi-functional partially linear regression models

“…On the one hand, (β 1 , β 2 ) T = (0, 0) T , this fact agreeing with the findings in Aneiros-Pérez and Vieu (2006), Maity and Huang (2012) and Aneiros-Pérez and Vieu (2013). On the other hand, both β 1 and β 2 are negative; that is, for a fixed absorbance curve, as the protein and/or the moisture contents increase (decrease), the fat content decreases (increases).…”

“…Specifically, fat, protein and moisture (water) contents (say Y , X 1 and X 2 , respectively) were measured, in percentages, on n = 215 food samples; in addition, the corresponding absorbance spectra (say ζ ) were recorded on a Tecator Infratec Food and Feed Analyzer working in the wavelength range 850-1050 nm (discretized on 100 channel spectrum of absorbances). This data set was analysed in Ferraty and Vieu (2006), Aneiros-Pérez and Vieu (2006) and Maity and Huang (2012), among others, from nonparametric, partial linear and partial linear varying coefficient models, respectively. It is available at http://lib.stat.cmu.edu/datasets/tecator, and the sample of curves, {ζ i } n i=1 , can be seen in Figure 3.…”

A Literature Review of Semi-functional Partial Linear Regression Models

“…And responses with missing-at-random (MAR) [71].  Varying Coefficient Models: There are some papers with extensions of varying coefficient models ,but we don't repeat them ,and we only select the following extensions: the partially varying coefficient models stratified by a functional covariate [72], varying coefficient partially functional linear regression model (VCPFLM) [73], partially functional linear varying coefficient model (PFLVCM) with a hypothesis and bootstrap [74], and the robust estimation based on the rank-based estimation [75].  Variable Selection: These papers are related to the variable selections methodologies: the variable selection with nonconcave-penalized least square in a high-dimensional partial linear regression model and with penalized composite quantile regression method [76,77], simultaneously consider multiple functional and scalar predictors and identify the important features [78], estimation and variable selection based on penalized regression estimators [79].…”

On semiparametric regression in functional data analysis

“…For instance, a general formulation of the partial linear functional model allowing to treat as well regression as median or quantile is proposed in Qingguo (2015). Also worth being mentioned is the contribution by Maity and Huang (2012) in which a similar model is studied with the specificity of using the functional covariates for stratifying. Finally, a mixture of partial linear and single index ideas is developed in Ding, Liu, Xu, and Zhang (2017), Wang, Feng, and Chen (2016), Yang, Lin, and Lian (2019), and Yu, Du, and Zhang (2020).…”