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Song, Qiongxia; Yang, Lijian

Spline confidence bands for variance functions. (English) Zbl 1165.62317

J. Nonparametric Stat. 21, No. 5, 589-609 (2009).
Summary: Asymptotically exact and conservative confidence bands are obtained for possibly heteroscedastic variance functions, using piecewise constant and piecewise linear spline estimation, respectively. The variance estimation is as efficient as an infeasible estimator when the conditional mean function is known, and the widths of the confidence bands are of optimal order. Simulation experiments provide strong evidence that corroborates the asymptotic theory while the computing is extremely fast. A slower bootstrap band is also proposed, with much higher accuracy. As illustration, the bootstrap spline band has been applied to test for heteroscedasticity in fossil data and in motorcycle data.

Cited in 22 Documents

MSC:

62G15 Nonparametric tolerance and confidence regions
62G08 Nonparametric regression and quantile regression
62G10 Nonparametric hypothesis testing
65C60 Computational problems in statistics (MSC2010)

Keywords:

B-spline; heteroscedasticity; infeasible estimator; knots; nonparametric regression; variance function
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References:

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