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Asymptotic normality of nearest neighbor regression function estimates. (English) Zbl 0539.62026
Summary: Let (X,Y) be a random vector in the plane. We show that a smoothed N.N. estimate of the regression function $$m(x)={\mathbb{E}}(Y| X=x)$$ is asymptotically normal under conditions much weaker than needed for the Nadaraya-Watson estimate. It also turns out that N.N. estimates are more efficient than kernel-type estimates if (in the mean) there are few observations in neighborhoods of x.

MSC:
 62E20 Asymptotic distribution theory in statistics 62J02 General nonlinear regression 62G05 Nonparametric estimation
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