Variance estimation in nonparametric regression via the difference sequence method

Details Variance estimation in nonparametric regression via the difference sequence method Variance estimation in nonparametric regression via the difference sequence method

2007-12-06

arxiv.org/abs/0712.0898v1

Annals of Statistics 2007, Vol. 35, No. 5, 2219-2232

Mathematics

Statistics Theory

Published in at http://dx.doi.org/10.1214/009053607000000145 the Annals of Statistics (http://www.imstat.org/aos/) by the Inst

Scientific paper

10.1214/009053607000000145

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.

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