Premium
Variance function partially linear single‐index models
Author(s) -
Lian Heng,
Liang Hua,
Carroll Raymond J.
Publication year - 2015
Publication title -
journal of the royal statistical society: series b (statistical methodology)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 6.523
H-Index - 137
eISSN - 1467-9868
pISSN - 1369-7412
DOI - 10.1111/rssb.12066
Subject(s) - variance function , heteroscedasticity , function (biology) , variance (accounting) , mathematics , linear model , parametric statistics , index (typography) , linear regression , statistics , computer science , accounting , evolutionary biology , world wide web , business , biology
Summary 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.