A smooth simultaneous confidence band for conditional variance function

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• 作者：Li Cai ; Lijian Yang
• 关键词：B spline ; Confidence band ; Heteroscedasticity ; Infeasible estimator ; Knots ; Nadaraya–Waston estimator ; Variance function ; 62G05 ; 62G08 ; 62G10 ; 62G15 ; 62G32
• 刊名：TEST
• 出版年：2015
• 出版时间：September 2015
• 年：2015
• 卷：24
• 期：3
• 页码：632-655
• 全文大小：823 KB
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• 作者单位：Li Cai (1)
  Lijian Yang (1)
  
  1. Center for Advanced Statistics and Econometrics Research, Soochow University, Suzhou, 215006, China
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Statistics
  Statistics
  Statistical Theory and Methods
  Statistics for Business, Economics, Mathematical Finance and Insurance
  
• 出版者：Springer Berlin / Heidelberg
• ISSN：1863-8260

文摘

A smooth simultaneous confidence band (SCB) is obtained for heteroscedastic variance function in nonparametric regression by applying spline regression to the conditional mean function followed by Nadaraya–Waston estimation using the squared residuals. The variance estimator is uniformly oracally efficient, that is, it is as efficient as, up to order less than \(n^{-1/2}\), the infeasible kernel estimator when the conditional mean function is known, uniformly over the data range. Simulation experiments provide strong evidence that confirms the asymptotic theory while the computing is extremely fast. The proposed SCB has been applied to test for heteroscedasticity in the well-known motorcycle data and Old Faithful geyser data with different conclusions.