Smooth Simultaneous Confidence Bands Of Conditional Variance Functions

A smooth simultaneous confidence band (SCB) is obtained for heteroscedastic variance function in nonparametric regression by applying spline regression to the con-ditional mean function followed by Nadaraya-Waston estimation using the squared residuals. The variance estimator is uniformly oracally efficient, that is, it is as effi-cient as, up to order less than n-1/2, the infeasible kernel estimator when the condi-tional 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.