A law of the iterated logarithm for nonparametric regression function estimators (Q1074976)
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scientific article; zbMATH DE number 3949495
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A law of the iterated logarithm for nonparametric regression function estimators |
scientific article; zbMATH DE number 3949495 |
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A law of the iterated logarithm for nonparametric regression function estimators (English)
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1984
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Let \(m_ n(x)\) be a Nadaraya-Watson kernel type estimator or a Legendre orthogonal polynomial estimator of an unknown regression function m(x), based on an i.i.d. sample. A pointwise law of the iterated logarithm is proved for \(m_ n(x)-m(x).\) These results are parallel to those of \textit{P. Hall} [Z. Wahrscheinlichkeitstheor. Verw. Geb. 56, 47-61 (1981; Zbl 0443.62027)] on density estimation, and extend those of \textit{K. Noda} [Ann. Inst. Stat. Math. 28, 221-234 (1976; Zbl 0369.62068)] on the strong consistency of kernel regression estimators.
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Nadaraya-Watson kernel type estimator
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Legendre orthogonal polynomial estimator
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pointwise law of the iterated logarithm
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density estimation
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strong consistency
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kernel regression estimators
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