Gaussian mixture density modeling and decomposition with weighted likelihood

A classic yet challenging research topic, Gaussian mixture density modeling and decomposition, is attracting much attention in a variety of disciplines. A Gaussian mixture density can be viewed as a contaminated Gaussian density with respect to each Gaussian component in the mixture. A component may not be well represented when the data is analyzed from a mixture density. In this article, Gaussian mixture density modeling and decomposition with weighted likelihood is studied. Then based on the Gaussian mixture density decomposition (GMDD) algorithm and weighted likelihood equations (WLEs), a new algorithm, called weighted Gaussian mixture density decomposition (WGMDD) algorithm is proposed. The WGMDD algorithm is effective and robust. It produces estimates with low bias and mean square error, and makes the applications of GMDD algorithm more extensive and more exact. A small simulation experiment illustrates the above point.