# 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