问题 : Semiparametric modeling and estimation of the dispersion function in regression

报告人：Prof.Ingrid Vankeilegom (Institute of Statistics, University catholique de Louvain ,Belgium)

时间：2009年2月23日（周一）下昼3：00-4：00

所在：伟易博新楼217课堂

Abstract :

Modeling heteroscedasticity in semiparametric regression can improve the efficiency of the estimator of the parametric component in the regression function, and is important for inference problems such as plug-in bandwidth selection and the construction of confidence intervals. However, the literature on exploring heteroscedasticity in a semiparametric setting is rather limited. Existing work is mostly restricted to the partially linear mean regression model with a fully nonparametric variance structure. The nonparametric modeling of heteroscedasticity is hampered by the curse of dimensionality in practice. Moreover, the approaches used in existing work need to assume smooth objective functions, therefore exclude the emerging important class of semiparametric quantile regression models. To overcome these drawbacks, we propose a general semiparametric location-dispersion regression framework, which enriches the currently available semiparametric regression models. With our general framework, we do not need to impose a special semiparametric form for the location or dispersion function. Rather, we provide easy to check sufficient conditions such that the asymptotic normality theory we establish is valid for many commonly used semiparametric structures, for instance, the partially linear structure and single-index structure. Our theory permits non-smooth location or dispersion functions, thus allows for semiparametric quantile heteroscedastic regression. We demonstrate the proposed method via simulations and the analysis of a real data set.