Department of Statistical Science

The Department of Statistics, which is located in the University’s Fox School of Business and Management, has 15 full-time graduate faculty members and about forty graduate students in its Master’s and Ph.D. programs.

Graduate Courses

5001: Quantitative Methods for Business (3 s.h.) This course is designed to introduce contemporary elementary applied statistics to provide an appreciation for the uses of statistics in business, economics, everyday life, as well as hands-on capabilities needed in other courses and professional employment.

5002: Introduction to BioStatistics (3 s.h.) Same statistical methods covered in Stat 5001 but illustrated with special emphasis on applications in health and biological sciences.

8001: Probability and Statistics Theory I (3 s.h.) (Prerequisite: Advanced calculus). Prerequisite: Advanced calculus. Topics include basic probability theory, random variables, standard probability distributions, Basics of asymptotic theory; limit theorems, statistical decision theory, sampling distribution, and distribution theory of order statistics.

8002: Probability and Statistics Theory II (3 s.h.) (Prerequisite: Stat. 8001). A comprehensive development of the theory of statistics, including, data reduction (sufficiency, completeness, ancillary statistics), estimation techniques (method of moments, least squares, maximum likelihood, Bayes estimation), theory of estimation (bias, sampling error, sampling distribution; best unbiased estimators; lower bounds on variance; consistency, large sample properties), hypothesis testing (likelihood ratio tests, Neyman-Pearson Theorem; p-values, power; Bayesian tests; unbiased and most powerful tests; score tests), interval estimation (pivotal quantities, inversion of tests; confidence intervals, Bayesian credible intervals; large sample confidence intervals), bootstrap resampling technique.

8003: Statistical Methods I (3 s.h.) (Prerequisite: Calculus). Introduction to applied statistics. Topics include basic concepts about probability, method of moments, MLE, EM-algorithm, confidence interval, hypothesis testing, nonparametric methods, and Bayesian methods with focus on methods and applications. The course requires heavy usage of R.

8004: Statistical Methods II (3 s.h.) (Prerequisite: Stat 8003 or permission of instructor). This course covers statistical methods including linear models and applications, analysis of multifactor experiments, linear mixed-effects models, generalized linear models. More topics including nonparametric smoothing and bootstrap will also be introduced if time permits.

8031: Probability and Large Sample Theory (Prerequisite: Stat 8001 and Stat 8104 or equivalent courses). An in-depth knowledge in real analysis is mandatory for this course. An advanced level theoretical course covering measure theoretic probability, some probability inequalities, statistical independence, strong and weak laws of large numbers, convergence theories, variance stabilizing transformations, characteristic functions, and central limit theorem.

8101: Stochastic Processes (3 s.h.) (Prerequisite: Stat 8001 or Stat 8112 or permission of instructor). After a review of some key concepts and properties of special distribution functions, the course will cover discrete-time Markov chains, Poisson point processes, random walks, martingales, renewal processes, wiener processes, Brownian motion, and diffusion processes. Examples from statistics, engineering, and finance will be used throughout the course.

8102: High-Dimensional Statistical Methods (3 s.h.) (Prerequisite: Stat 8004 or permission of instructors). High-dimension statistical methods for analyzing large and complex data sets will be introduced in the framework of linear and generalized linear models. Main topics include methods for penalized estimations, variable and model selection, covariance/correlation matrices estimations with applications, and inferences with high-dimensional statistical methods.

8103: Theory and Methods of Sample Surveys (3 s.h.) (Prerequisite: Undergraduate statistics courses and completion or currently enrolled in Stat 8001 and 8003). This course covers basic theory of design and estimation of sample surveys on finite population. Topics include concepts of probability sampling, simple random, systematic, stratified, clustered, multistage and other probability sampling methods. Methods including Horvitz-Thompson estimation of totals, means, proportions, and regression coefficients and model assisted ratio and regression estimations, replication method for variance estimation will be introduced. More topics, e.g. nonresponse effect and imputation will be covered if time permits.

8104: Mathematics for Statistics (3 s.h.) (Prerequisite: undergraduate calculus and linear algebra or permission of instructor). Vector spaces and subspaces; linear independence; rank of a matrix; special matrices like orthogonal, idempotent, nilpotent, Hadamard, and Givens, partitioned matrices; determinant; inverse and g-inverse; solutions of linear equations; Eigenvalues and eigenvectors; diagonalization theorems; quadratic forms and optimization; sets; Sigma Field, Lebesgue, and probability measures; limits and continuity of functions; derivatives and partial derivatives; mean value theorem; Taylor’s expansion; maxima and minima of functions; infinite sequences and series with tests of convergence; integration of several variables; gamma and beta integrals; Sterling’s formula; fundamental inequalities; some results on optimization and approximation of functions.

8105: Time Series Analysis I (3 s.h.) (Prerequisite: Stat. 8002 or 8004 or permission of instructor).This course covers theory and application of univariate time series analysis, and both time domain and frequency domain methods. Topics include stationary and nonstationary linear processes, time series model building, forecasting, unit root test, intervention models and outlier detection, spectral theory of stationary processes, spectral windows, and estimation of spectrum. Projects using software are required

8106: Generalized Linear Models I (3 s.h.) (Prerequisite: Stat. 8002, Stat 8004 and Stat. 8104 or permission of instructor). Covers the basic theory and practice of generalized linear models (GLM), the logistic, Poisson, and gamma regression, as well as models for multilevel or longitudinal Gaussian responses, such as the hierarchical linear model and linear mixed model. The students will work with R and/or SAS throughout the semester.

8107: Design of Experiments I (3 s.h.) (Prerequisite: Stat. 8004 or permission of instructor). Principles of experimental designs, completely randomized designs, multiple comparisons, randomized block design, Latin square designs, missing value problems, analysis of covariance, and factorial experiments.

8108: Applied Multivariate Analysis I (3 s.h.) (Prerequisite: Stat. 8001, 8003, and 8104, or permission of instructor). Multivariate normal distribution, marginal and conditional distributions, estimation of population mean vector and dispersion matrix; correlation, partial correlation, and multiple correlation coefficients, Hotelling’s T2; MANOVA, discriminant function, repeated measurements analysis, principal components and canonical correlation, factor analysis, and multidimensional scaling.

8109: Regression, Time Series, and Forecasting for Business Applications (does not carry credit for MS or PhD in Statistics) (3 s.h.) (Prerequisite: Stat. 5001 or 5002 or permission of instructor). Intermediate level course that covers regression analysis, time series analysis, and forecasting. The course is application oriented and standard statistical packages such as MINITAB are introduced and extensively used.

8111: Survey Techniques for Business Applications (does not carry credit for PhD in Statistics) (3 s.h.) (Prerequisite: Stat. 5001 or 5002 or permission of instructor). Application oriented. A course dealing with statistical and non-statistical aspects of organizing a sample survey. Included are discussions of objectives, measurement, sample selection, pilot testing, data collection, data editing, summarization, and interpretation of results, in addition to describing the various sampling schemes. Students may be required to plan and execute a survey.

8112: Statistical Theory for Business Research (may substitute for 8001-8002 for MS in Statistics, does not carry credit for PhD in Statistics) (3 s.h.) (Prerequisite: calculus). The course covers a variety of statistical theory and methods illustrating with applications in business. Random variables, joint and conditional probability distributions, sampling distributions, estimation and testing of hypotheses, regression and nova analyses, chi-squared methods of association.

8113: Statistical Methods for Business Research (does not carry credit for MS or PhD in Statistics) (3 s.h.) (Prerequisite: Stat 8112 or equivalent). Topics covered in this course are: multiple linear regressions, ANOVA, logistic regression models, Poison regression models, multinomial regression models, factor analysis and Bayesian statistics. The course requires heavy usage of R.

8114: Survival Analysis I (3 s.h.) (Prerequisite: Stat 8002 or 8004 with instructor’s permission). Life tables, parametric and nonparametric methods for estimating hazard and survival functions, inference with Cox proportional hazard model with covariates.

8115: Nonparametric Methods (3 s.h.) (Prerequisite: Stat 8002 or 8004 with instructor’s permission). Nonparametric statistical methods, estimation and testing of hypothesis when the function form of the population distribution is not completely specified.

8116: Categorical Data Analysis. (3 s.h.) (Prerequisite: Stat. 8002 or 8004 with permission of instructor). Sampling models and analyses for discrete data, Fisher’s exact test, logistic regression, ROC analysis, log-linear models and Poisson regression, conditional logistic regression, Cochran-Mantel-Hansel test; measures of agreement between observers, quasi-independence, multinomial logic models, proportional odds model, association models, generalized estimating equations (GEE), generalized linear mixed model (GLIMMIX), GSK models, composite link functions. The students will need to work with R and/or SAS throughout the semester.

8117: Clinical Trials (3 s.h.) (Prerequisite: Stat. 8002 or 8004 with permission of instructor). Introduction to the special problems associated with medical trials on humans. Topics include randomization, sample-size determination, methods for early trial termination, and tests for superiority, equivalence, and non-inferiority. Also discussed are choice of endpoints, control of side effects, and use of historical data, meta-analysis, and ethics of experimentation on humans.

8121: Statistical Computing (3 s.h.) (Prerequisites: Stat. 8003 or permission of instructor). Topics include: floating point architecture, random number generation, design of statistical software, computational linear algebra, numerical integration, optimization methods.

8122: Advanced SAS Programming (3 s.h.).

8123: Time Series Analysis and Forecasting (3 s.h) (Prerequisite: Stat 8002 or 8004 or permission of instructor). A time series analysis with financial and business applications. Topics include important univariate and multivariate time series methods including ARIMA models, intervention analysis, outlier detection, time series regression, volatility and GARCH models, vector time series and cointegration. Projects using software are required.

8982: Independent Study (1-3 s.h.) (Prerequisite: Departmental Approval). Normally for 1 credit with maximum 3 credits. Special study in statistics theory and methods under the direct supervision of a graduate faculty member. No more than three semester hours of independent study may be counted toward MS degree requirements.

9001: Advanced Statistical Inference I (3 s.h.) (Prerequisite: Advanced Calculus, Stat 8001-8002, or 8031 or equivalents). Background: Matrix Theory. Estimation: sufficiency, completeness, UMVU Estimation, information inequality, invariance principle, Bayes estimation, admissibility, maximum likelihood estimation, large sample properties of estimators.

9002: Advanced Statistical Inference II (3 s.h.) (Prerequisite: Stat. 9001). Topics include testing of hypotheses, Neyman-Pearson Fundamental Lemma, uniformly most powerful tests, confidence intervals, likelihood ratio tests, asymptotic tests, multiple hypotheses testing, EM algorithm, bootstrap, multiple testing, etc. in addition to the standard statistical inference topics.

9101: Time Series Analysis II (3 s.h.) (Prerequisite: Stat. 8105 or its equivalent or permission of instructor). This course covers theory and application of multiple time series analysis and special topics, including transfer function models, time series regression, vector time series models, cointegration, multivariate GARCH models, multivariate spectral analysis, state space models, long memory and nonlinear processes, time series aggregation and disaggregation, repeated measurements, space-time modeling, high dimensional time series problems, and others. Projects using software are required.

9103: Statistical Learning and Data Mining (3 s.h.) (Prerequisite: statistical theory and methods (e.g., Statistics 8001, 8002, 8003, and 8004) or with permission of instructor; a good knowledge of matrix algebra, of at least one of packages: S-PLUS, R, MATLAB, SAS, SPSS). This course includes topics such as multiple regression, prediction accuracy and model assessment, crossvalidation, bootstrap, biased regression methods, principal components regression, partial least-squares regression, ridge regression, shrinkage estimators, multivariate reduced-rank regression, neural networks, principal components, canonical variates, projection pursuit, multidimensional scaling and distance geometry, linear discrimination and classification, support vector machines and kernel methods, Decision trees for regression and classification, combining classifiers by begging, boosting, and random forests, nonlinear dimensionality reduction, nonlinear manifold learning, and clustering algorithms. Emphasis will be on working with large data sets obtained from data mining, machine learning, and bioinformatics applications.

9106: Generalized Linear Models II (3 s.h.) (Prerequisite: Stat. 8106 or permission of instructor). Continuation of Stat 8106 covers the theory and practice of analyzing multivariate repeated/correlated non-Gaussian responses, with or without missing observations. Missing at random (MAR) models; informative missingness; EM algorithm; multiple imputations; quasi-likelihood estimation; generalized estimating equations (GEE); transition models; Gibbs sampling; Markov Chain Monte-Carlo (MCMC) technique. The students will need to work with R, SAS and WinBugs throughout the semester.

9107: Design of Experiments II (3 s.h.) (Prerequisite: Stat. 8107 or with permission of instructor). Covers symmetric and asymmetrical factorial experiments, fractional replication, split plot design, balanced and partially balanced incomplete block designs without and with recovery of inter block information and lattice designs.

9108: Multivariate Analysis II (3 s.h.) (Prerequisite: Stat. 9002 and 8108 or with permission of instructor) Specialized topics in multivariate analysis.

9114: Survival Analysis II (3 s.h.) (Prerequisite: Statistics 8114 or with permission of instructor) Applications of advanced tools such as martingale theory in survival analysis.

9116: Statistical Genetics: an advanced graduate course (Prerequisite: Stat 8001, 8002, 8003 and 8004 or equivalent courses) A basic knowledge in R and/or SAS is mandatory for this course. An advanced level graduate course in statistical genetics covering the Basic concepts of allele, gene, genotype, phenotype, Hardy-Weinberg equilibrium, linkage analysis, QTL mapping using marker analysis, functional mapping for longitudinal traits, analysis of ultra-high dimensional data, genome-wide association studies.

9180: Seminar in New Topics in Statistics (3 s.h.) (Prerequisite: Permission of instructor) Special topics in Statistics.

9183: Directed Study in Statistics (variable credit) (Prerequisite: departmental permission)

9190: Seminar in New Topics in Statistics (3 s.h.) (Prerequisite: Permission of instructor) Special topics in Statistics.

9994: Directed Study in Statistics (variable credit) (Prerequisite: departmental permission) Preparation for proposal (preliminary) examinations.

9998: Directed Study in Statistics (variable credit) (Prerequisite: departmental permission) 

9999: Dissertation Research (1-12 s.h.) (Prerequisite: departmental approval)