Adaptive kernel density estimation with generalized least square cross-validation

Year 2019, Volume: 48 Issue: 2, 616 - 625, 01.04.2019

Serdar Demir

Abstract

Adaptive kernel density estimator is an efficient estimator when the density to be estimated has long tail or multi-mode. They use varying bandwidths at each observation point by adapting a fixed bandwidth for data. It is well-known that bandwidth selection is too important for performance of kernel estimators. An efficient recent method is the generalized least square cross-validation which improves the least squares cross-validation. In this paper, performances of the adaptive kernel estimators obtained based on the generalized least square cross-validation are investigated. We performed a simulation study to inform about performances of the modified adaptive kernel estimators. For the simulation, we use also the bandwidth selection methods of normal reference, least squares cross-validation, biased cross-validation, and plug-in methods. Simulation study shows that the adaptive kernel estimators improve the performances of the kernel estimators with fixed bandwidth selected based on generalized least square cross-validation.

Keywords

Kernel density estimation, Adaptive bandwidth, Cross-validation

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