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A law of the iterated logarithm for nearest neighbor regression function estimator. (English) Zbl 0792.62031

Summary: Let \((X,Y)\) be an \(\mathbb{R}^ d\times \mathbb{R}^ 1\)-valued random variable. We establish a law of the iterated logarithm for the nearest neighbor estimator of the regression function \(m(x)= E(Y\mid X=x)\). This result gives the sharp rates of pointwise strong consistency of the estimator. Our conditions on \(m(x)\) and the distribution of \(X\) are much weaker than those needed for Nadaraya-Watson’s kernel estimate and S.-S. Yang’s [J. Am. Stat. Assoc. 76, 658-662 (1981; Zbl 0475.62031)] neighbor type estimate.

MSC:

62G07 Density estimation
62G20 Asymptotic properties of nonparametric inference
60F15 Strong limit theorems

Citations:

Zbl 0475.62031
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