Mathematical Statistics

Basic information

Workload: 

45 hours

Prerequisite: 

Does not exist.

Syllabus: 

Statistical Models: Elements of Decision Theory. Bayesian Models. Prediction. Sufficiency. Exponential Models. Methods of Estimation: Minimum contrast estimates. Estimating equations. Weighted least squares. Empirical plug-in estimates. Maximum likelihood. Criteria: Minimax. Bayes. Unbiased. Information Inequality. Robustness. Testing and confidence regions: The Neyman-Pearson Lemma. Uniformly most Powerful Tests. Monotone Likelihood Ratio Models. The Duality between Tests and Confidence Regions. Bayesian Formulations. Likelihood Ratio Procedures. Prediction Intervals. Asymptotic approximations. Consistency. The Delta Method. Asymptotic Normality of Estimates. Asymptotic efficiency of the maximum likelihood estimate.

Bibliography

Mandatory: 

·       Shao, J. (2003). Mathematical statistics. Springer.
·       Lehmann, E. L., & Casella, G. (2006). Theory of point estimation. Springer Science & Business Media.
·       Bickel, P. J., Doksum, K. A. (1977). Mathematical statistics: basic ideas and selected topics. Englewood Cliffs, NJ: Prentice Hall.

Complementary: 

·       Keener, R. W. (2011). Theoretical statistics: Topics for a core course. Springer.
·       Schervish, M. J. (2012). Theory of statistics. Springer Science & Business Media.
·       Bernardo, J. M. e Smith, A. F. M. (1994). Bayesian Theory. Wiley.
·       Lehmann, E. L., & Romano, J. P. (2005). Testing Statistical Hypotheses. Springer.
·       Le Cam, L., & Yang, G. L. (2012). Asymptotics in statistics: some basic concepts. Springer Science & Business Media.