### Qualifying Exam on Statistical Inference

The qualifying exam on statistical inference is an open book exam --- you can use whatever books and notes you bring with you. You can use a calculator (but not a computer). You should bring tables giving cdf probabiities for the standard normal distribution, and critical values for the standard normal, T, and chi-square distributions.

The exam covers material in the following parts of the book Statistical Inference, 2nd Ed., by George Casella and Roger L. Berger:
• some topics in probability
• Sec. 3.4 (exponential families)
• Sec. 3.5 (location and scale families)
• subsection 5.5.1 (convergence in probability)
• subsection 5.5.3 (convergence in distribution)
• subsection 5.5.4 (the delta method)
• principles of data reduction (sufficient statistics and the likelihood principle)
• Sec. 6.1
• Sec. 6.2
• Sec. 6.3 (excluding subsection 6.3.2)
• point estimation
• Ch. 7 (excluding subsection 7.2.4)
• hypothesis testing
• Sec. 8.1
• subsection 8.2.1
• subsection 8.3.1
• subsection 8.3.2
• subsection 8.3.4
• subsection 8.3.5
• interval estimation
• Sec. 9.1
• subsection 9.2.1
• subsection 9.2.2
• subsection 9.2.3
• subsection 9.3.1
• asymptotics
• subsection 10.1.1
• subsection 10.1.2
• subsection 10.1.3
• Section 10.3
• Section 10.4
While the exam can pertain to any parts of the book listed above, the majority of the exam will focus on common methods of point estimation (e.g., the method of moments, maximum likelihood, and estimation using UMVUEs) and hypothesis testing (e.g., likelihood ratio tests based on the Neyman-Pearson lemma and other types of likelihood ratio tests). Also, the exam committee which prepares the exam each semester typically likes to include something about interval estimation, and also a problem which makes use of some sort of asymptotic result pertaining to testing or estimation (e.g., using the asymptotic normality of a maximum likelihood estimator to obtain an approximate confidence interval, or perform a Wald test). The focus is on being able to use estimation and testing methods (i.e., derive estimates and tests based on various parametric models) instead of on proofs (although on some exams there may be a problem or two with something similar to a proof).