Maximum L q -Likelihood Estimation via the Expectation-Maximization Algorithm: A Robust Estimation of Mixture Models

Yichen Qin and Carey E. Priebe

Journal of the American Statistical Association, 2013, vol. 108, issue 503, 914-928

Abstract: We introduce a maximum L q -likelihood estimation (ML q E) of mixture models using our proposed expectation-maximization (EM) algorithm, namely the EM algorithm with L q -likelihood (EM-L q ). Properties of the ML q E obtained from the proposed EM-L q are studied through simulated mixture model data. Compared with the maximum likelihood estimation (MLE), which is obtained from the EM algorithm, the ML q E provides a more robust estimation against outliers for small sample sizes. In particular, we study the performance of the ML q E in the context of the gross error model, where the true model of interest is a mixture of two normal distributions, and the contamination component is a third normal distribution with a large variance. A numerical comparison between the ML q E and the MLE for this gross error model is presented in terms of Kullback--Leibler (KL) distance and relative efficiency.

Date: 2013
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Citations: View citations in EconPapers (4)

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DOI: 10.1080/01621459.2013.787933

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