Variance function partially linear single-index models
Heng Lian, Hua Liang, Raymond J. Carroll
Journal of the Royal Statistical Society: Series B (Statistical Methodology) · 2015 · Volume 77 · Issue 1
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.
Keywords
Asymptotic theory, Estimating equation, Identifiability, Kernel regression, Modelling ozone levels, Partially linear single-index model, Semiparametric efficiency, Single-index model, Variance function estimation
Enable JavaScript for citation tools and additional paper interactions.