Variance function partially linear single-index models

• 成果类型: Article
• 署名作者: Lian, Heng; Liang, Hua; Carroll, Raymond J.
• 署名单位: Nanyang Technological University; George Washington University; Texas A&M University System; Texas A&M University College Station
• 刊物名称: JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY
• ISSN/ISSBN: 1369-7412
• DOI: 10.1111/rssb.12066
• 发表日期: 2015
• 页码: 171-194
• 关键词: dimension reduction; regression; heteroscedasticity; estimators; robust

摘要

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.