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November 2013 Optimal variance estimation without estimating the mean function
Tiejun Tong, Yanyuan Ma, Yuedong Wang
Bernoulli 19(5A): 1839-1854 (November 2013). DOI: 10.3150/12-BEJ432

Abstract

We study the least squares estimator in the residual variance estimation context. We show that the mean squared differences of paired observations are asymptotically normally distributed. We further establish that, by regressing the mean squared differences of these paired observations on the squared distances between paired covariates via a simple least squares procedure, the resulting variance estimator is not only asymptotically normal and root-$n$ consistent, but also reaches the optimal bound in terms of estimation variance. We also demonstrate the advantage of the least squares estimator in comparison with existing methods in terms of the second order asymptotic properties.

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Tiejun Tong. Yanyuan Ma. Yuedong Wang. "Optimal variance estimation without estimating the mean function." Bernoulli 19 (5A) 1839 - 1854, November 2013. https://doi.org/10.3150/12-BEJ432

Information

Published: November 2013
First available in Project Euclid: 5 November 2013

zbMATH: 1281.62105
MathSciNet: MR3129036
Digital Object Identifier: 10.3150/12-BEJ432

Rights: Copyright © 2013 Bernoulli Society for Mathematical Statistics and Probability

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Vol.19 • No. 5A • November 2013
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