An alternative quasi likelihood approach,Bayesian analysis and data-based inference for model specification |
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| Institution: | 1. Department of Statistics, The University of Auckland, Private Bag 92019, Auckland, New Zealand;2. School of Mathematics and Statistics, University of St Andrews, St Andrews KY16 9SS, UK;1. School of Mathematics and Statistics, Chongqing Technology and Business University, Chongqing 400067, China;2. Institute of Chinese Financial Studies, Southwestern University of Finance and Economics, Chengdu 610074, China;1. Department of Finance, Kellogg School of Management, Northwestern University, Evanston, IL 60208, United States;2. Department of Economics, Duke University, Durham, NC 27708, United States;1. Department of Risk Management and Insurance, Georgia State University, United States;2. Department of Statistics, London School of Economics, United Kingdom;1. Department of Mathematics, Hong Kong Baptist University, Hong Kong;2. School of Public Health, The University of Hong Kong, Hong Kong;3. Department of Biostatistics and Bioinformatics, Duke University, USA;4. CEMSE Division, King Abdullah University of Science and Technology, Saudi Arabia;1. Fakultät für Mathematik, Ruhr-Universität Bochum, Germany;2. Statistical Sciences Research Institute, University of Southampton, UK |
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| Abstract: | This paper studies an alternative quasi likelihood approach under possible model misspecification. We derive a filtered likelihood from a given quasi likelihood (QL), called a limited information quasi likelihood (LI-QL), that contains relevant but limited information on the data generation process. Our LI-QL approach, in one hand, extends robustness of the QL approach to inference problems for which the existing approach does not apply. Our study in this paper, on the other hand, builds a bridge between the classical and Bayesian approaches for statistical inference under possible model misspecification. We can establish a large sample correspondence between the classical QL approach and our LI-QL based Bayesian approach. An interesting finding is that the asymptotic distribution of an LI-QL based posterior and that of the corresponding quasi maximum likelihood estimator share the same “sandwich”-type second moment. Based on the LI-QL we can develop inference methods that are useful for practical applications under possible model misspecification. In particular, we can develop the Bayesian counterparts of classical QL methods that carry all the nice features of the latter studied in White (1982). In addition, we can develop a Bayesian method for analyzing model specification based on an LI-QL. |
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| Keywords: | Quasi likelihood Model misspecification Limited information Bayesian methods Sandwich covariance Large sample correspondence Model selection |
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