Kernel Density Estimators for Gaussian Mixture Models
Tomas Ruzgas
Kaunas University of Technology, Lithuania
Indrė Drulytė
Kaunas University of Technology, Lithuania
Published 2013-12-20


nonparametric density estimators
kernel method
Monte Carlo method
adaptive smoothing
symmetric mean absolute percentage error

How to Cite

Ruzgas T. and Drulytė I. (2013) “Kernel Density Estimators for Gaussian Mixture Models”, Lithuanian Journal of Statistics, 52(1), pp. 14-21. doi: 10.15388/LJS.2013.13919.


The problem of nonparametric estimation of probability density function is considered. The performance of kernel estimators based on various common kernels and a new kernel K (see (14)) with both fixed and adaptive smoothing bandwidth is compared in terms of the symmetric mean absolute percentage error using the Monte Carlo method. The kernel K is everywhere positive but has lighter tails than the Gaussian density. Gaussian mixture models from a collection introduced by Marron and Wand (1992) are taken for Monte Carlo simulations. The adaptive kernel method outperforms the smoothing with a fixed bandwidth in the majority of models. The kernel K shows better performance for Gaussian mixtures with considerably overlapping components and multiple peaks (double claw distribution).

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