Abstract: In this paper a new method of selecting the smoothing parameter in nonparametric regression called median cross validation (MCV) is suggested. This method is applied to choose the number of nearest neighbors used in estimating the regression function by local sample medians. Uniform strong consistency is obtained under reasonable conditions. MCV is effective in dealing with outliers in the data. Simulation results are given to demonstrate its superiority over other methods.
Key words and phrases: Cross-validation, median, nearest neighbor median estimates, uniformly strong consistency.