Program Description: Doctor of Philosophy

The Ph.D. course requirements are sufficiently flexible to allow the student to pursue either a methodological or theory oriented plan of study. The student, in consultation with his/her adviser and Ph.D. advisory committee, can design a course of study to adequately prepare for his/her chosen dissertation topic.

CORE COURSE REQUIREMENTS

a. ST 720, ST 730

b. Three additional statistics lecture courses at the 700 level. (ST 721, 722, 725, 731, 740, 750, 760, 770)

c) ST 799 (Dissertation)

(Students may take any of the courses ST 721, ST 722, ST 731, and/or ST 740 twice provided there is no overlap in course content. However, such course(s) may only be counted once in meeting the Ph.D. credit requirement of the Graduate School. Students are expected to register for ST 792, Seminar, each semester.)

ADDITIONAL COURSE WORK

The student is expected to meet with his/her Ph.D. advisory committee for the purpose of selecting the remainder of his/her course work. This meeting should take place prior to the completion of the student's program of study (Graduate School Form GS-6). Written approval of the student's program of study by the advisory committee is required. Every student is expected to take at least one lecture course each semester. (The University requires a total of 72 credits for the Ph.D. degree, of which a maximum of 30 credits may be carried over from the master's degree.)

EXAMINATIONS

THE DOCTORAL CANDIDACY REQUIREMENT (DCR)

A student is considered to be part of the formal Ph.D. program once he/she has successfully completed the Doctoral Candidacy Requirement (DCR). The DCR consists of two components: two mandatory examinations described in (a) and (b) below; and a particular demonstrated competency described in (c) below.

a. An examination in probability and mathematical statistics based on the course content of ST 520 and ST 530.

b. An examination in statistical methods and linear models based on the course content of ST 540 and ST 640.

The above two examinations are administered once each year in August, prior to the start of the fall semester. Students should attempt both of these examinations the August after completion of their first full year in the graduate program. A second attempt to pass either or both of these examinations is allowed at the next offering.

c) Competence in a choice of two subjects from sampling, time series, and stochastic processes (based on the course content of ST 605, ST 525, and ST 521, respectively) must be demonstrated. This may be accomplished by obtaining at least an A minus (A-) grade in the corresponding course or, if the student should get less than an A minus (A-) in such course, the student will receive one and only one chance to pass a Candidacy Examination on the same subject within thirteen (13) months from the end of the course. A student who does not take the relevant course at Colorado State University can demonstrate competency by taking the Candidacy examination and will be granted a second chance if he/she should not pass the first taking of the exam.

PhD PRELIMINARY EXAMINATION

The Ph.D. preliminary examination is an oral exam administered by the student's graduate advisory committee after having passed ST 720 and ST 730. The Graduate School requires that this examination be administered at least two terms before the final dissertation defense.

DOCTORAL DISSERTATION

A satisfactory dissertation must be completed, approved by the student's graduate advisory committee, and defended in a final oral examination which is open to the University community. The dissertation must constitute original research in statistical theory or applications and must be submitted in a form acceptable to the Graduate School. The student's dissertation results must be presented in a Departmental seminar.

CATALOG DESCRIPTIONS OF 700-LEVEL COURSES

ST 720. 4(4-0-0). Probability Theory. S. Prerequisites: ST 520, M 517. Measure theoretic probability, characteristic functions; convergence; laws of large numbers; central limit, extreme value, asymptotic theory.

ST 721. 3(3-0-0). Applied Probability and Stochastic Processes I. F, S. Prerequisite: ST 720. General theory of processes; Markov processes in discrete and continuous time; review of martingales, random walk; renewal and regenerative processes; stationary processes.

ST 722. 3(3-0-0). Applied Probability and Stochastic Processes II. F, S, SS. Prerequisite: ST 720. Brownian motion, diffusion, stochastic differential equations; weak convergence and central limit theorems. Applications in engineering, natural sciences.

ST 725. 3(3-0-0). Time Series and Stationary Processes. F, S, SS. Prerequisite: ST 720, ST 730. Spectral theory of multivariate stationary processes; estimation, testing for spectral, linear, ARMA representations; best linear predictors, filters.

ST 730. 4(4-0-0). Advanced Theory of Statistics I. F. Prerequisites: ST 530, ST 720. Minimal sufficiency, maximal invariance; Neyman-Pearson theory; Fisher, Kullback-Leibler information; asymptotic properties of maximum-likelihood methods.

ST 731. 3(3-0-0). Advanced Theory of Statistics II. S, SS. Prerequisite: ST 730. Decision-theory model; Bayes, e-Bayes, complete, and admissible classes; applications to sequential analysis and design of experiments.

ST 740. 3(3-0-0). Advanced Statistical Methods. F, S. Prerequisite: ST 640, concurrent registration in ST 730. Generalized additive models; recursive partitioning regression and classification; graphical models and belief networks, spatial statistics.

ST 750. 3(3-0-0). Advanced Theory of Design. F, S. Prerequisite: ST 650 or written consent of instructor. Information theory; design evaluation, factorial designs and optimal designs, orthogonal and balanced arrays, designs with discrete/continuous factors.

ST 760. 3(3-0-0). Theory of Multivariate Statistics. F, SS. Prerequisite: ST 640, concurrent registration in ST 730. Theory of multivariate normal; maximum-likelihood inference, union-intersection testing for single sample; theory of a multivariate linear model.

ST 770. 3(3-0-0). Approximation Theory and Methods. F,S. Prerequisite: ST 720, ST 730. Edgeworth expansions, saddlepoint methods; applications of weak convergence and other approximation methods in mathematical statistics.

ST 792. 1(0-0-1). Seminar.

ST 795. Variable credit. Independent Study.

ST 796. Variable credit. Group Study. Methodology, stochastic processes, experimental design, multidimensional statistics.

ST 799. Variable credit. Dissertation.