Qualifying Examination Guidelines

Guidelines for the Theory Examination

Casella G and Berger RL (1990). Statistical Inference . Wadsworth & Brooks/Cole.

Cox DR and Hinkley DV (1974). Theoretical Statistics . Chapman and Hall.

Lehmann EL (1983). Theory of Point Estimation. Wiley.

Ross SA (1994). A First Course in Probability , Fourth Edition. MacMillan.

While it is not possible to provide an exhaustive list, the following list of topics is offered as a guideline for the types of questions that are asked on the theory exam:

• Probability & Distribution Theory
• Probability Calculations (marginal, conditional, expectations, etc.)
• Distributions of Functions of Random Variables
• Properties of Common Discrete & Continuous Exp. Family dns, Univariate & Multivariate
• Generating Functions (moment generating functions, characteristic functions, probability generating functions)
• Inequalities
• Convergence Concepts
• Limit Theorems (Strong and Weak Laws of Large Numbers, Central Limit Theorem)
• Inference
• General Principles (sufficiency, ancillarity, consistency, completeness, etc.)
• Point Estimation - UMVU, method of moments, estimating equations, maximum likelihood, conditional and quasi-likelihood
• Interval Estimation (construction of confidence intervals and Bayes credibility intervals)
• Classical Hypothesis Testing (UMP tests, likelihood ratio tests, Type I & II errors, score & Wald tests, power/sample size calculations), loss functions
• Asymptotic Distribution Theory (Delta method, Regularity Conditions)
• Maximum Likelihood
• Properties
• Calculations
• Numerical Algorithms (scoring, EM, etc.)
• Variance Estimation
• Bayes
• Bayes' theorem, Bayesian credibility intervals, Bayesian hypothesis testing, conjugate priors, empirical Bayes

Guidelines for the Applications Examination

Dobson AJ (1990). An Introduction to Generalized Linear Models . Chapman & Hall.

Diggle PJ, Liang KY, and Zeger SL (1994). Analysis of Longitudinal Data , Chapters 1-4 and 6. Oxford University Press.

Draper N and Smith H (1981). Applied Regression Analysis , Second Edition. Wiley.

Hosmer DW and Lemeshow S (1989). Applied Logistic Regression , Chapters 1-3, 5, and 6.Wiley.

Weisberg S (1985). Applied Linear Regression , Second Edition. Wiley.

While it is not possible to provide an exhaustive list, the following list of topics is offered as a guideline for the types of questions that are asked on the applications exam:

• Linear Regression
• Assumptions, model diagnostics, goodness-of-fit measures
• Estimation/Prediction/Hypothesis Testing/Interval Estimation
• Model formulation and interpretation of parameters
• Other modeling issues - variable selection, multicollinearity, transformations, interaction, multiple comparisons
• ANOVA/ANCOVA for Regression
• Mixed Models/Repeated Measures
• Formulation of mean and covariance structures, parameter interpretation
• Estimation and inference for fixed and random effects
• Estimation methods (ML, REML, GEE)
• Model assumptions, goodness-of-fit
• ANOVA for mixed models
• Unbalanced and missing data
• Generalized Linear Models
• Assumptions
• Link Functions for Standard Exponential Family Distributions
• Estimation/Hypothesis Testing/Interval Estimatio
• Interpretation of Parameters
• Diagnostics/Goodness-of-fit
• Models for ordinal data
• Chi-squared tests for contingency tables
• Experimental Design
• Design of randomized and observational studies
• Analysis plans that account for design features
• Power/sample size calculations