The Real Numbers (Natural Numbers and Induction, Ordered Fields, Ordered Fields, Topology of the Real Numbers, Compact Sets).

Basic concepts of decision theory, sufficiency and completeness; completeness of multiparametric exponential family; unbiasedness and invariance of decision rules; Bayes, minimax and invariant estimators; testing of hypotheses and optimality properties.

Probability spaces, extension theorem, random variables; independence, conditional probability, conditional expectation; laws of large numbers, law of the iterated logarithm; convergence in distribution; characteristic functions; central limit theorems; martingales.

Theory and data analysis involving likelihood functions, mixed models, missing responses.

Supervised reading and discussion of a selected research topic. May be repeated to a maximum of nine credits.

Supervised reading and discussion of a selected research topic. May be repeated to a maximum of nine credits.

Half-time to full-time work on thesis. May be repeated to a maximum of six semesters.

Half-time to full-time work on dissertation. May be repeated to a maximum of six semesters.

Residency credit for preparing and taking the qualifying examination. Students may register for one semester of this course in anticipation of completing the qualifying examination during the semester. The course is not repeatable and is not required.

Residency credit for dissertation research after the qualifying examination. Students may register for this course in the semester of the qualifying examination. A minimum of two semesters are required as well as continuous enrollment (Fall and Spring) until the dissertation is completed and defended.