Abstract: Given that y_i=f\left(x_i\right)+\varepsilon_i, i=1,2, \cdots, n, let \hatf(\boldsymbolx) be the nearest neighbour estimate of regressive function f(x), and h_n^* the cross-validation seleotion of the number of neighbours. Ker-Ohau \mathrmLi^5 studied the limiting behaviour of mean square errors \widehatE_r r\left(h_n^*\right)=\frac1n\left\|F_n-\widehatF_n\right\|_n_n^2 and obtained under cartain conditions the \lim _n \rightarrow \infty \widehatE_r r\left(h_n^*\right)=U(P), where \boldsymbolF_n=\left(f\left(x_1\right), \cdots, f\left(x_n\right)\right)^\prime and \hatF_n=\left(\hatf\left(x_1\right), \cdots, \hatf\left(x_n\right)\right)^\prime. Under the assumption that the \varepsilon_i^\prime s are i.i.d., we improve the results of 5.