Asymptotic normality of nearest neighbor regression function estimates. (English) Zbl 0539.62026

Stute, Winfried

Ann. Stat. 12, 917-926 (1984).

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

Keywords:

nearest neighbor estimates; asymptotic normality; regression function; Nadaraya-Watson estimate; kernel-type estimates