title: Variance Function Partially Linear Single-Index Models1.
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: Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore 637371, Singapore. henglian@ntu.edu.sg.
authors: Heng
authors: H
authors: Lian
authors: Department of Statistics, George Washington University, Washington, D.C. 20052, U.S.A.
authors: Hua
authors: H
authors: Liang
authors: Department of Statistics, Texas A&M University, College Station, TX 77843-3143, USA carroll@stat.tamu.edu.
authors: Raymond J
authors: RJ
authors: Carroll
keywords: Asymptotic theory; Estimating equation; Identifiability; Kernel regression; Modeling ozone levels; Partially linear single index model; Semiparametric efficiency; Single-index model; Variance function estimation
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