, Volume 24, Issue 3, pp 632–655

A smooth simultaneous confidence band for conditional variance function

Original Paper

DOI: 10.1007/s11749-015-0427-5

Cite this article as:
Cai, L. & Yang, L. TEST (2015) 24: 632. doi:10.1007/s11749-015-0427-5


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.


B spline Confidence band Heteroscedasticity Infeasible estimator Knots Nadaraya–Waston estimator Variance function 

Mathematics Subject Classification

62G05 62G08 62G10 62G15 62G32 

Copyright information

© Sociedad de Estadística e Investigación Operativa 2015

Authors and Affiliations

  1. 1.Center for Advanced Statistics and Econometrics ResearchSoochow UniversitySuzhouChina

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