Minimax estimation of a bounded squared mean (Q1185328)
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scientific article; zbMATH DE number 38220
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Minimax estimation of a bounded squared mean |
scientific article; zbMATH DE number 38220 |
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Minimax estimation of a bounded squared mean (English)
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28 June 1992
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Let \(X_ 1,X_ 2,\dots,X_ n\) be a random sample from \(N(\theta,\sigma^ 2)\) distribution, and suppose that \(|\theta|\leq\tau\) where \(\tau\) is known. The author studies the minimax estimation of \(\theta^ 2\) under squared error loss, and obtains an asymptotic expression for the minimax risk. This result has an application in nonparametric estimation of quadratic functionals.
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normal mean
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Gaussian white noise
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normal model
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unknown mean
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Gaussian white noise model
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hardest 1-dimensional subproblems
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minimax estimation
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squared error loss
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asymptotic expression for the minimax risk
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estimation of quadratic functionals
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