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Variance estimation in nonparametric regression via the difference sequence method
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DOI：10.1214/009053607000000145.png)
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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.
Keyword:
nonparametric regression
variance estimation
asymptotic minimaxity
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3.7
论文数:
2.8K
被引数:
2.9W
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On difference-based variance estimation in nonparametric regression when the covariate is high dimensional协变量为高维时非参数回归中基于差异的方差估计
PREAI
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