Variance estimation in nonparametric regression via the difference sequence method
نویسندگان
چکیده
منابع مشابه
Variance Estimation in Nonparametric Regression via the Difference Sequence Method
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 ...
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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 ...
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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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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 ...
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Estimating the residual variance is an important question in nonparametric regression. Among the existing estimators, the optimal difference-based variance estimation proposed in Hall, Kay, and Titterington (1990) is widely used in practice. Their method is restricted to the situation when the errors are independent and identically distributed. In this paper, we propose the optimal difference-b...
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ژورنال
عنوان ژورنال: The Annals of Statistics
سال: 2007
ISSN: 0090-5364
DOI: 10.1214/009053607000000145