Course Description

Course Name

Statistical Theory and Inference

Session: VCPF3119

Hours & Credits

24 Host University Units

Prerequisites & Language Level

Taught In English

  • There is no language prerequisite for courses at this language level.

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 content subject to change