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Statistica Sinica 33 (2023), 237-258

MODEL SELECTION OF GENERALIZED ESTIMATING
EQUATION WITH DIVERGENT MODEL SIZE

Shicheng Wu1 , Xin Gao1 and Raymond J. Carroll2

1York University and 2Texas A &M University

Abstract: We consider the problem of model selection for a high-dimensional generalized estimating equation (GEE) in a marginal regression analysis for clustered or longitudinal data. Because the GEE method only makes assumptions about the first two moments, the full likelihood is not specified. Therefore, the likelihood-based model selection criteria cannot be applied directly. This paper introduces a generalized model selection criterion based on a quadratic form of the residuals. Using the large deviation result of the quadratic forms, we choose appropriate penalty terms on the model complexity. Lastly, we establish the model selection consistency of the proposed criterion for a divergent number of covariates.

Key words and phrases: Generalized estimation equation, generalized information criterion, large deviation, model selection consistency.

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