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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 locationscale 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]. 1 3 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]. 2