an:03858171
Zbl 0539.62026
Stute, Winfried
Asymptotic normality of nearest neighbor regression function estimates
EN
Ann. Stat. 12, 917-926 (1984).
00149160
1984
j
62E20 62J02 62G05
nearest neighbor estimates; asymptotic normality; regression function; Nadaraya-Watson estimate; kernel-type estimates
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.