Variance function partially linear single-index models

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Author(s)

Detail(s)

Original languageEnglish
Pages (from-to)171-194
Journal / PublicationJournal of the Royal Statistical Society. Series B: Statistical Methodology
Volume77
Issue number1
Online published8 Apr 2014
Publication statusPublished - Jan 2015
Externally publishedYes

Abstract

We consider heteroscedastic regression models where the mean function is a partially linear single-index model and the variance function depends on a generalized partially linear single-index model. We do not insist that the variance function depends only on the mean function, as happens in the classical generalized partially linear single-index model. We develop efficient and practical estimation methods for the variance function and for the mean function. Asymptotic theory for the parametric and non-parametric parts of the model is developed. Simulations illustrate the results. An empirical example involving ozone levels is used to illustrate the results further and is shown to be a case where the variance function does not depend on the mean function.

Research Area(s)

  • Asymptotic theory, Estimating equation, Identifiability, Kernel regression, Modelling ozone levels, Partially linear single-index model, Semiparametric efficiency, Single-index model, Variance function estimation