# Statistical Theory and Inference

University of Cape Town

## Course Description

• ### Course Name

Statistical Theory and Inference

• ### Host University

University of Cape Town

• ### Location

Cape Town, South Africa

Statistics

• ### Language Level

Taught In English

• ### Prerequisites

Course entry requirements: (MAM1000W or MAM1012S) and STA1006Sf

• ### Course Level Recommendations

Lower

ISA offers course level recommendations in an effort to facilitate the determination of course levels by credential evaluators.We advice each institution to have their own credentials evaluator make the final decision regrading course levels.

### Hours & Credits

• Host University Units

24
• Recommended U.S. Semester Credits
4
• Recommended U.S. Quarter Units
6
• ### Overview

Course outline:
STA2004F is a rigorous introduction to the foundation of the mathematical statistics and aims to provide students with a deeper understanding of the statistical concepts covered in STA1006S. The course is intended for students studying Mathematical Statistics or Actuarial Science. STA2004F is divided into two broad sections: (1) Distribution theory and (2) Statistical Inference. During the first part of the course, students will learn to derive the distributions of random variables and their transformations, and explore the limiting behaviour of sequences of random variables. The last part of the course covers the estimation of population parameters and hypothesis testing based on a sample of data.
Distribution Theory: Univariate and bivariate distributions. Conditional distributions. Moments. Generating functions (moment, probability and cumulative). Convergence in distribution and central limit theorem. Transformations of random variables. Sampling distributions from the normal distribution (chi-squared, t, F). Order statistics.
Statisitcal Inference: Paremeter estimation. Methods of moments. Maximun likelihood. Asymptotic theory. Efficiency and sufficiency. The exponential family. Hypothesis testing. Confidence intervals.

### Course Disclaimer

Credits earned vary according to the policies of the students' home institutions. According to ISA policy and possible visa requirements, students must maintain full-time enrollment status, as determined by their home institutions, for the duration of the program.