14.385. Midterm. 1 Question 1. (30 minutes) (a) Briefly explain the Skorohod representation for linear quantile re-gression model. Explain some special cases (location or location-scale models). (b) Briefly explain the equivariance to monotone transformations that quantile regression models have and conditional mean models don’t. State some interesting examples. 2 Question 2. (30 minutes) (a) What is the bootstrap bias correction method? State the pseudo-code for bias correction. (b) Briefly explain when the bootstrap might fail. Cite as: Victor Chernozhukov, course materials for 14.385 Nonlinear Econometric Analysis, Fall 2007. MIT OpenCourseWare (http://ocw.mit.edu), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY]. 13 Question 3. (30 minutes) (a) Explain briefly what Bayesian estimators do. Explain what poste-rior mean, median, and quantiles are. (b) Are posterior mean and medians inferior estimators compared to the maximum likelihood estimators? Are they consistent, asymp-totically normal? Brief answers suffice. Cite as: Victor Chernozhukov, course materials for 14.385 Nonlinear Econometric Analysis, Fall 2007. MIT OpenCourseWare (http://ocw.mit.edu), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].
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