Estimation in the presence of many nuisance parameters: Composite likelihood and plug-in likelihood

Billy Wu, Qiwei Yao and Shiwu Zhu

Stochastic Processes and their Applications, 2013, vol. 123, issue 7, 2877-2898

Abstract: We consider the incidental parameters problem in this paper, i.e. the estimation for a small number of parameters of interest in the presence of a large number of nuisance parameters. By assuming that the observations are taken from a multiple strictly stationary process, the two estimation methods, namely the maximum composite quasi-likelihood estimation (MCQLE) and the maximum plug-in quasi-likelihood estimation (MPQLE) are considered. For the MCQLE, we profile out nuisance parameters based on lower-dimensional marginal likelihoods, while the MPQLE is based on some initial estimators for nuisance parameters. The asymptotic normality for both the MCQLE and the MPQLE is established under the assumption that the number of nuisance parameters and the number of observations go to infinity together, and both the estimators for the parameters of interest enjoy the standard root-n convergence rate. Simulation with a spatial–temporal model illustrates the finite sample properties of the two estimation methods.

Keywords: Composite likelihood; Incidental parameters problem; Nuisance parameter; Panel data; Profile likelihood; Quasi-likelihood; Root-n convergence; Spatial autoregressive model; Stationary process; Time series; U-statistic (search for similar items in EconPapers)
Date: 2013
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DOI: 10.1016/j.spa.2013.03.017

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