A New Kernel Estimator Based on Scaled Inverse Chi-Squared Density Function

Abstract

In this work, a new kernel estimator based on scaled inverse chi-squared distribution is proposed to estimate densities having nonnegative support. The optimal rates of convergence for the mean squared error (MSE) and the mean integrated squared error (MISE) are obtained. Adaptive Bayesian bandwidth selection method with Lindley approximation is used for heavy tailed distributions. Simulation studies are performed to compare the performance of the average integrated square error (ISE) by using the bandwidths obtained from the global least squares cross-validation bandwidth selection method and the bandwidths obtained from adaptive Bayesian method with Lindley approximation. Finally, real data sets are presented to illustrate the findings.