Nested coordinate descent algorithms for empirical likelihood
Empirical likelihood (EL) as a nonparametric approach has been demonstrated to have many desirable merits. While it has intensive development in methodological research, its practical application is less explored due to the requirements of intensive optimizations. Effective and stable
algorithms therefore are highly desired for practical implementation of EL. This paper bears the effort to narrow the gap between methodological research and practical application of EL. We try to tackle the computation problems, which are considered difficult by practitioners, by introducing
a nested coordinate descent algorithm and one modified version to EL. Coordinate descent as a class of convenient and robust algorithms has been shown in the existing literature to be effective in optimizations. We show that the nested coordinate descent algorithms can be conveniently and
stably applied in general EL problems. The combination of nested coordinate descent with the MM algorithm further simplifies the computation. The nested coordinate descent algorithms are a natural and perfect match with inferences based on profile estimation and variable selection in high-dimensional
data. Extensive examples are conducted to demonstrate the performance of the nested coordinate descent algorithms in the context of EL.
Keywords: 62G05; 65K10; MM algorithm; confidence regions; cyclic coordinate descent; empirical likelihood; likelihood ratio; profiled empirical likelihood
Document Type: Research Article
Affiliations: 1: Business School, University of Colorado, Denver, CO, 80204, USA 2: Department of Epidemiology and Biostatistics, University of Maryland, College Park, MD, 20742, USA
Publication date: 02 September 2014
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