MAT 3046 - INTRO TO MATHEMATICAL STATISTICS

credits: 3.0
This course serves as a calculus and probability-based introduction to the theory and practice of mathematical statistics. In this course, students will learn: estimation theory; hypothesis testing, including likelihood ratio tests; linear models and least-squares estimation; the analysis of variance and its applications; the analysis of categorical data (time permitting; the theory of nonparametric statistics; and the Bayesian approach to statistical inference. Objectives: A) Compute point-estimates, their bias and their standard errors, their confidence intervals; and proved theorems about them; B) Develop and compute various measures of the quality of point-estimators: bias, relative efficiency, consistency, and sufficiency; and establish the connection between efficiency and sufficiency (Rao-Blackwell Theorem); C) Develop the general testing paradigm and used it to perform various hypothesis tests; develop and computed measures of the quality of a test, such as the power; develop the likelihood ratio test paradigm and used it to perform hypothesis tests; D) Develop linear models and the method of least-squares, and used these to conduct inferential procedures; E) Apply the techniques of mathematical statistics in the analysis of variance, the analysis of categorical data (time permitting); F) Develop and perform procedures for non-parametric statistics, both based on ranks and on runs; G) Develop the theory of Bayesian statistics and used it to compute estimates and to test hypotheses. Method of Instruction: Lecture, discussion, homework, computer exercises, data collection and analysis. Method of Evaluation: Homework 40%, Exams (midterm and final) 40%, Data collection 10%, and Computer exercises 10%.

Prerequisite(s): MAT 3045 - INTRODUCTION TO PROBABILITY