Uniformity in \(h\) in the functional limit law for the increments of the empirical process indexed by functions (Q1776845)
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scientific article; zbMATH DE number 2167781
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Uniformity in \(h\) in the functional limit law for the increments of the empirical process indexed by functions |
scientific article; zbMATH DE number 2167781 |
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Uniformity in \(h\) in the functional limit law for the increments of the empirical process indexed by functions (English)
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12 May 2005
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The article studies the almost sure convergence of kernel density estimators uniformly in the bandwidth \(h_n \leq h \leq \tilde h_n\) and the kernel \(K\), where \(h_n\) and \(\tilde h_n\) satisfy certain growth conditions and \(K \in {\mathcal F}\), with \({\mathcal F}\) denoting a family of functions fulfilling appropriate boundedness, support and entropy assumptions.
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kernel density estimator
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uniform consistency
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