On estimation of maximum values of nonparametric signals for random fields (Q2739829)
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scientific article; zbMATH DE number 1646307
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On estimation of maximum values of nonparametric signals for random fields |
scientific article; zbMATH DE number 1646307 |
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16 September 2001
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signal processing
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minimax risk
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On estimation of maximum values of nonparametric signals for random fields (English)
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Let the random field \(X_\varepsilon(t)\) be described by the model NEWLINE\[NEWLINEdX_\varepsilon(t)=S(t)dt+\varepsilon dW(t),NEWLINE\]NEWLINE where \(W(t)\) is a Wiener field observed on \(t\in[0,1]^n\). The problem is to estimate \(\sup_{t\in[0,1]^n}S(t)\) when \(S\) satisfies some Hölder conditions. A lower bound for the minimax risk is obtained and an asymptotically efficient estimator (as \(\varepsilon\to 0\)) is constructed which is the sup of a kernel smoothed observed trajectory of \(X_\varepsilon\).
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0.8052730560302734
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0.763491153717041
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