Variable bandwidth Kernel estimator of the mode

Abstract

In this paper, the problem of estimating the mode of a probability density function has been studied.  Parzen (1962) proposed a kernel estimator of the mode depends on a single bandwidth. In this paper, the Parzen estimator has been improved by proposing a kernel estimator with variable bandwidth for the mode of the density function. Proceeding as in Parzen (1962), the consistency and asymptotic normality of the proposed estimator are shown. Moreover, the good  performance of the proposed estimator is tested via simulation study and it is shown that the proposed estimator is more efficient than the Parzen estimator.