Variance estimation in nonparametric regression via the difference sequence method (short title: Sequence-based variance estimation)
نویسنده
چکیده
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. ∗AMS 2000 Subject Classification 62G08, 62G20 †
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Variance estimation in nonparametric regression via the difference sequence method ( short title :
Consider the standard Gaussian nonparametric regression problem. The observations are (xi, yi) where and where ~i are iid with finite fourth moment p4 < oo. This article presents a class of difference-based kernel estimators for the variance *AMS 2000 Subject Classification 62G08, 62G20 t ~ e ~ w o r d s and Phrases: Nonparametric regression, Variance estimation, Asymptotic minimaxity he work o...
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