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Variance estimation in nonparametric regression via the difference sequence method

Statistics Theory 2009-09-29 v1 Statistics Theory

Abstract

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.

Keywords

Cite

@article{arxiv.0712.0898,
  title  = {Variance estimation in nonparametric regression via the difference sequence method},
  author = {Lawrence D. Brown and M. Levine},
  journal= {arXiv preprint arXiv:0712.0898},
  year   = {2009}
}

Comments

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

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