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

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• 作者：Billy Wu^a ; Qiwei Yao^a ; ^b ; ^{q.yao@lse.ac.uk} ; Shiwu Zhu^c
• 关键词：Composite likelihood ; Incidental parameters problem ; Nuisance parameter ; Panel data ; Profile likelihood ; Quasi-likelihood ; Root-nn convergence ; Spatial autoregressive model ; Stationary process ; Time series ; UU-statistic
• 刊名：Stochastic Processes and their Applications
• 出版年：2013
• 出版时间：July, 2013
• 年：2013
• 卷：123
• 期：7
• 页码：2877-2898
• 全文大小：270 K

文摘

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- convergence rate. Simulation with a spatial-temporal model illustrates the finite sample properties of the two estimation methods.