Simultaneous confidence bands for comparing variance functions of two samples based on deterministic designs

Chen Zhong and Lijian Yang
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Chen Zhong: Tsinghua University

Computational Statistics, 2021, vol. 36, issue 2, No 18, 1197-1218

Abstract: Abstract Asymptotically correct simultaneous confidence bands (SCBs) are proposed in both multiplicative and additive form to compare variance functions of two samples in the nonparametric regression model based on deterministic designs. The multiplicative SCB is based on two-step estimation of ratio of the variance functions, which is as efficient, up to order $$n^{-1/2}$$ n - 1 / 2 , as an infeasible estimator if the two mean functions are known a priori. The additive SCB, which is the log transform of the multiplicative SCB, is location and scale invariant in the sense that the width of SCB is free of the unknown mean and variance functions of both samples. Simulation experiments provide strong evidence that corroborates the asymptotic theory. The proposed SCBs are used to analyze several strata pressure data sets from the Bullianta Coal Mine in Erdos City, Inner Mongolia, China.

Keywords: Brownian motion; B-spline; Kernel; Oracle efficiency; Strata pressure; Variance ratio (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1007/s00180-020-01043-6

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