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)
- Convergence Concepts
- Limit Theorems (Strong and Weak Laws of Large Numbers, Central Limit Theorem)
- 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
- Numerical Algorithms (scoring, EM, etc.)
- Variance Estimation
- Bayes' theorem, Bayesian credibility intervals, Bayesian hypothesis testing, conjugate priors, empirical Bayes
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
- Link Functions for Standard Exponential Family Distributions
- Estimation/Hypothesis Testing/Interval Estimatio
- Interpretation of Parameters
- 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