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Understanding Misspecified Models and Model-Constrained Estimation in Statistics

This presentation explores the intricacies of misspecified models and model-constrained estimation, focusing on their implications for experimental design and statistical inference. Drawing on the foundational works of notable statisticians like Norbert Wiener, Hirotugu Akaike, and Halbert White, we delve into the crucial aspects of problem setting, KL divergence, and the asymptotic properties of maximum likelihood estimates. Additionally, we highlight the importance of understanding model mis-specification and its practical applications in research.

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Understanding Misspecified Models and Model-Constrained Estimation in Statistics

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  1. Arnau Tibau Puig October 10th 2008 Misspecified models and Model-constrained estimation

  2. « What most experimenters take for granted before they begin their experiments is infinitely more interesting than any results to which their experiments lead. » Norbert Wiener (1894-1964)‏ What's this going to be about.

  3. (about the order of the group meetings)‏ Ami: you're the second. Arnau: Why me, why me? Ami: you're the second. That's why I'm talking, so: - no results - no nice theories - just some ideas from papers Seriously.

  4. Problem setting Misspecified model (definition)‏ Facts about KL divergence [Akaike 1974] Model-constrained Estimation What? Why? Useful asymptotic (big n) results for misspecified models Asymptotics of MLE [LeCam 1953] [Huber 1967] and [White 1982] results Regularity... Idea of the proofs And so what? GMT approach [GMT 1984] Outline

  5. [LeCam 1953] On some asymptotic properties of maximum likelihood estimates and related Bayes. University of California publications in Statistics, 1 (1953)‏ [Huber 1967] The behavior of the maximum likelihood estimates under nonstandard conditions. Huber P., Proceedings of 5th Berkley Symposium on Mathematica Statistics and Probability, 1967 [Akaike 1974] A new Look at the statistical model identification. Hirotugu Akaike, IEEE Transactions on Automatic Control, vol. 19 no. 6 [White 1982] Maximum Likelihood Estimation of Misspecified Models, Halbert White, Econometrica, Vol. 50, No. 1 (Jan., 1982), pp. 1-25 [GMT 1984] Pseudo Maximum Likelihood Methods: Theory C. Gourieroux, A. Monfort and A. Trognon Econometrica, Vol. 52, No. 3 (May, 1984), pp. 681-700 Very good tutorial on Misspecified Models: Stas Kolnikov, 2007 web.missouri.edu/~kolenikovs/talks/Stas-misspecified-handout.pdf - References

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