Variance Function Partially Linear Single-Index Models1. Academic Article

abstract

• We consider heteroscedastic regression models where the mean function is a partially linear single index model and the variance function depends upon a generalized partially linear single index model. We do not insist that the variance function depend only upon 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 nonparametric parts of the model is developed. Simulations illustrate the results. An empirical example involving ozone levels is used to further illustrate the results, and is shown to be a case where the variance function does not depend upon the mean function.

authors

• Carroll, Raymond

published proceedings

• J R Stat Soc Series B Stat Methodol

author list (cited authors)

• Lian, H., Liang, H., & Carroll, R. J.

citation count

• 31

complete list of authors

• Lian, Heng||Liang, Hua||Carroll, Raymond J

publication date

• January 2015

publisher

• Oxford University Press (OUP)  Publisher

published in

• Journal of the Royal Statistical Society Series B: Statistical Methodology  Journal

keywords

• Asymptotic Theory
• Estimating Equation
• Identifiability
• Kernel Regression
• Modeling Ozone Levels
• Partially Linear Single Index Model
• Semiparametric Efficiency
• Single-index Model
• Variance Function Estimation

PubMed Central ID

• 25642139

Digital Object Identifier (DOI)

• 10.1111/rssb.12066

start page

• 171

end page

• 194

volume

• 77

issue

• 1

URL

• http%3A%2F%2Fdx.doi.org%2F10.1111%2Frssb.12066