Detecting heteroscedasticity in non-parametric regression using weighted empirical processes

• 成果类型: Article
• 署名作者: Chown, Justin; Mueller, Ursula U.
• 署名单位: Ruhr University Bochum; 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.12282
• 发表日期: 2018
• 页码: 951-974
• 关键词: testing heteroscedasticity; variance function; parametric form; models; heteroskedasticity; checks

摘要

Heteroscedastic errors can lead to inaccurate statistical conclusions if they are not properly handled. We introduce a test for heteroscedasticity for the non-parametric regression model with multiple covariates. It is based on a suitable residual-based empirical distribution function. The residuals are constructed by using local polynomial smoothing. Our test statistic involves a detection function' that can verify heteroscedasticity by exploiting just the independence-dependence structure between the detection function and model errors, i.e. we do not require a specific model of the variance function. The procedure is asymptotically distribution free: inferences made from it do not depend on unknown parameters. It is consistent at the parametric (root n) rate of convergence. Our results are extended to the case of missing responses and illustrated with simulations.