Robust estimation in familial and longitudinal models

Bari, Wasimul (2007) Robust estimation in familial and longitudinal models. Doctoral (PhD) thesis, Memorial University of Newfoundland.

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Abstract

There exists many studies on the robust estimation of the regression effects in a linear model set up for continuous such as Gaussian data possibly containing one or more outliers. The robust estimation of the regression effects in a generalized linear model (GLM) set up for the count and binary data in the presence of outliers is, however, relatively difficult. In this thesis, we deal with this difficult estimation issue and develop the robust estimation procedures under three scenarios. First, a fully standardized Mallows-type quasi-likelihood (FSMQL) estimation technique is developed to obtain consistent regression estimates in the GLM set up for both independent count and binary data. Secondly, we develop a robust generalized quasi-likelihood (RGQL) estimation procedure to deal with the outliers in the generalized linear mixed model (GLMM) set up for both count and binary data. Finally, we also develop the RGQL estimation procedure to deal with possible outliers in the GLM set up for the longitudinal count and binary data. The performances of the proposed robust estimators are examined through extensive simulation studies under all three set up: the GLM for the independent count and binary data; the GLMM for the familial count and binary data; and the GLM for the longitudinal count and binary data.

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