Almost Sure Convergence of The k-NN Regression Estimate under Mixing condition

Abstract

In this work we will establish almost sure convergence for k-nearest neighbor estimate of the regression function under some mixing conditions. Our results will extend some previous results in the i.i.d case to the dependent case. In addition, we will conduct a simulation study using R software program to display the importance and influence of the sample size (n) on behavior of the estimator. For this purpose, the mean squares error criterion (MSE) was used.