Projection-type estimation for varying coefficient regression models

TL;DR

This paper introduces a new projection-based estimation method for varying coefficient regression models, providing efficient algorithms, asymptotic properties, and advantages over existing methods.

Contribution

It proposes a novel projection approach for estimating coefficient functions, with proven convergence, asymptotic distributions, and oracle properties, applicable to derivatives and various polynomial orders.

Findings

Algorithm converges at a geometric rate

Estimators have oracle properties

Advantages over marginal integration estimators

Abstract

In this paper we introduce new estimators of the coefficient functions in the varying coefficient regression model. The proposed estimators are obtained by projecting the vector of the full-dimensional kernel-weighted local polynomial estimators of the coefficient functions onto a Hilbert space with a suitable norm. We provide a backfitting algorithm to compute the estimators. We show that the algorithm converges at a geometric rate under weak conditions. We derive the asymptotic distributions of the estimators and show that the estimators have the oracle properties. This is done for the general order of local polynomial fitting and for the estimation of the derivatives of the coefficient functions, as well as the coefficient functions themselves. The estimators turn out to have several theoretical and numerical advantages over the marginal integration estimators studied by Yang, Park, Xue and H\"{a}rdle [J. Amer. Statist. Assoc. 101 (2006) 1212--1227].