  In regression analysis one wants to estimate the regression function from a
data. In this paper we consider the rate of convergence for the nearest
neighbor estimator in case that the regression function is $(p,C)$-smooth. It
is an open problem whether the optimal rate can be achieved by some nearest
neighbor estimator in case that $p$ is on (1,1.5]. We solve the problem
affirmatively. This is the main result of this paper. Throughout this paper, we
assume that the data is independent and identically distributed and as an error
criterion we use the expected $L_2$ error.
