The Finite Sample Performance of Modified Adaptive Kernel Estimators for Probability Density Function
Serpil Cula
Department of Insurance and Risk Management, Faculty of Commercial Sciences, Baskent University, Ankara, Turkey.
Serdar Demir *
Department of Statistics, Faculty of Sciences, Mugla Sitki Kocman University, Mugla, Turkey.
Oniz Toktamis
Department of Statistics, Faculty of Science, Hacettepe University, Ankara, Turkey.
*Author to whom correspondence should be addressed.
Abstract
It is well-known that the most popular probability density estimator is kernel density estimator in literature. Adaptive kernel density estimators are generally preferred for data with long tailed densities. In this paper, the adaptive kernel estimators for probability density function are studied. A modified adaptive kernel estimator is investigated. For finite sample performance comparisons, the root mean squared errors of the fixed and the adaptive kernel estimations are computed for simulated samples from various density distributions. The simulation results show that the modified adaptive kernel density estimators have better performance than the classical adaptive kernel density estimator.
Keywords: Density estimation, kernel estimator, adaptive kernel estimator, variable bandwidth