The Annals of Statistics

Variance estimation in nonparametric regression via the difference sequence method

Lawrence D. Brown and M. Levine

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Consider a Gaussian nonparametric regression problem having both an unknown mean function and unknown variance function. This article presents a class of difference-based kernel estimators for the variance function. Optimal convergence rates that are uniform over broad functional classes and bandwidths are fully characterized, and asymptotic normality is also established. We also show that for suitable asymptotic formulations our estimators achieve the minimax rate.

Article information

Ann. Statist., Volume 35, Number 5 (2007), 2219-2232.

First available in Project Euclid: 7 November 2007

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62G08: Nonparametric regression 62G20: Asymptotic properties

Nonparametric regression variance estimation asymptotic minimaxity


Brown, Lawrence D.; Levine, M. Variance estimation in nonparametric regression via the difference sequence method. Ann. Statist. 35 (2007), no. 5, 2219--2232. doi:10.1214/009053607000000145.

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