Estimating the Conditional Mode Using the Symmetrized Nearest Neighbor Kernel Estimator

Abstract

In this paper, the kernel estimation of the mode of a conditional probability density function is studied. We propose the Symmetrized Nearest Neighbor (SNN) kernel estimator to estimate the conditional mode. We study the asymptotic properties of the proposed estimator. Also, we derive its asymptotic normality under some conditions much weaker than that needed for the Nadaraya- Watson (NW) kernel estimator. The performance of the SNN kernel estimator is tested using three simulated and real data which indicate that the proposed estimator is reasonably good. In addition, a comparison between the proposed estimator and the NW estimator is given. Keywords Kernel Estimation, Conditional Mode, Nearest Neighbor Estimator, Nadaraya-Watson Estimator, Asymptotic Properties.