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Generalized estimating equations for mixtures with varying concentrations
Author(s) -
Maiboroda Rostyslav,
Sugakova Olena,
Doronin Alexey
Publication year - 2013
Publication title -
canadian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.804
H-Index - 51
eISSN - 1708-945X
pISSN - 0319-5724
DOI - 10.1002/cjs.11170
Subject(s) - mathematics , asymptotic distribution , parametric statistics , generalized estimating equation , nonparametric statistics , statistics , nuisance parameter , parametric model , gee , estimating equations , covariance matrix , distribution (mathematics) , covariance , dispersion (optics) , mixing (physics) , mathematical analysis , estimator , physics , quantum mechanics , optics
A finite mixture model is considered in which the mixing probabilities vary from observation to observation. A parametric model is assumed for one mixture component distribution, while the others are nonparametric nuisance parameters. Generalized estimating equations (GEE) are proposed for the semi‐parametric estimation. Asymptotic normality of the GEE estimates is demonstrated and the lower bound for their dispersion (asymptotic covariance) matrix is derived. An adaptive technique is developed to derive estimates with nearly optimal small dispersion. An application to the sociological analysis of voting results is discussed. The Canadian Journal of Statistics 41: 217–236; 2013 © 2013 Statistical Society of Canada