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