Instructor: Jimin Ding;
Office Hours: Wed. 1:30-3:00pm. or by appointment
Topics covered:
An introduction to Semiparametric statistics: I. Empiirical process techniques including: stochastic convergence, entropy calculations, Glivenko-Cantelli theorems, Donsker theorems, the functional delta method, Z-estimators and M-estimators; II. Semiparametric inference including: semiparametric models and efficiency, score functions and estimating equations, Maximum Likelihood Estimation (MLE), semiparametric MLE, profile likelihood, semiparametric M estimators, with applications to Cox Model and proportional odds model.
Prerequisites:
Math 5051 (measure theory) and Math 493 (or other equivalent probability course), or permission of the instructor.
Textbook:
Michael R. Kosorok
Introduction to Empirical Processes and Semiparametric Inference
Springer, 2008.
Some useful links and references:
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P.J. Bickel, C.A.J. Klaassen, Y. Ritov and J. Wellner (1998), Efficient and Adaptive Estimation for Semiparametric Models, Springer, New York.
- D. Pollard (1990), Empirical Processes: Theory and Applications, Volume 2 of NSF-CBMS Regional Conference Series in Probability and Statistics. Institute of Mathematical Statistics and Americian Statistical Association, Hayward, California.
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A. van der Vaart and J. Wellner (1996), Weak Convergence and Empirical Processes: With Applications to Statistics, Springer, New York.
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A. van der Vaart (1998), Asymptotic Statistics, Cambridge University Press, New York.
Collaboration:
Collaboration on homework can be helpful and hence is encouraged. However, you must do all written work by yourself. No collaboration is allowed in the take-home final.