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Minimum Hellinger Distance Estimation for k‐Component Poisson Mixture with Random Effects
Author(s) -
Xiang Liming,
Yau Kelvin K. W.,
Van Hui Yer,
Lee Andy H.
Publication year - 2008
Publication title -
biometrics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.298
H-Index - 130
eISSN - 1541-0420
pISSN - 0006-341X
DOI - 10.1111/j.1541-0420.2007.00920.x
Subject(s) - hellinger distance , mathematics , poisson distribution , random effects model , outlier , statistics , restricted maximum likelihood , count data , poisson regression , estimation theory , population , medicine , meta analysis , demography , sociology
Summary The k‐component Poisson regression mixture with random effects is an effective model in describing the heterogeneity for clustered count data arising from several latent subpopulations. However, the residual maximum likelihood estimation (REML) of regression coefficients and variance component parameters tend to be unstable and may result in misleading inferences in the presence of outliers or extreme contamination. In the literature, the minimum Hellinger distance (MHD) estimation has been investigated to obtain robust estimation for finite Poisson mixtures. This article aims to develop a robust MHD estimation approach for k‐component Poisson mixtures with normally distributed random effects. By applying the Gaussian quadrature technique to approximate the integrals involved in the marginal distribution, the marginal probability function of the k‐component Poisson mixture with random effects can be approximated by the summation of a set of finite Poisson mixtures. Simulation study shows that the MHD estimates perform satisfactorily for data without outlying observation(s), and outperform the REML estimates when data are contaminated. Application to a data set of recurrent urinary tract infections (UTI) with random institution effects demonstrates the practical use of the robust MHD estimation method.