Hong, Shengyan A law of the iterated logarithm for nearest neighbor regression function estimator. (English) Zbl 0792.62031 Northeast. Math. J. 9, No. 2, 173-184 (1993). 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 Keywords:nonparametric regression; kernel estimator; law of the iterated logarithm; nearest neighbor estimator; sharp rates of pointwise strong consistency; Nadaraya-Watson’s kernel estimate Citations:Zbl 0475.62031 PDFBibTeX XMLCite \textit{S. Hong}, Northeast. Math. J. 9, No. 2, 173--184 (1993; Zbl 0792.62031)