Document Type

Journal Article

Department/Unit

Department of Mathematics

Title

Shrinkage estimation analysis of correlated binary data with a diverging number of parameters

Language

English

Abstract

For analyzing correlated binary data with high-dimensional covariates, we, in this paper, propose a two-stage shrinkage approach. First, we construct a weighted least-squares (WLS) type function using a special weighting scheme on the non-conservative vector field of the generalized estimating equations (GEE) model. Second, we define a penalized WLS in the spirit of the adaptive LASSO for simultaneous variable selection and parameter estimation. The proposed procedure enjoys the oracle properties in high-dimensional framework where the number of parameters grows to infinity with the number of clusters. Moreover, we prove the consistency of the sandwich formula of the covariance matrix even when the working correlation matrix is misspecified. For the selection of tuning parameter, we develop a consistent penalized quadratic form (PQF) function criterion. The performance of the proposed method is assessed through a comparison with the existing methods and through an application to a crossover trial in a pain relief study. © 2013 Science China Press and Springer-Verlag Berlin Heidelberg.

Keywords

adaptive LASSO, correlated binary data, diverging number of parameters, GEE, oracle properties, penalized quadratic form function, sandwich covariance formula, variable selection

Publication Date

2013

Source Publication Title

Science China-Mathematics

Volume

56

Issue

2

Start Page

359

End Page

377

Publisher

Science Press

DOI

10.1007/s11425-012-4564-y

Link to Publisher's Edition

http://dx.doi.org/10.1007/s11425-012-4564-y

ISSN (print)

16747283

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