Mathematical Methods for Statistics and Econometrics - Uni. of Birmingham

This module introduces students to the theoretical underpinnings of statistical methodology and concentrates on inferential procedures within the framework of parametric models. The module is organised in three parts: The first part includes core topics in the theory of probability such as counting methods, sample space and events, axioms of probability, conditional probability, random variables, discrete and continuous probability distributions, multivariate probability distributions, the central limit theorem, among others. The second part includes core topics in estimation and inference, such as properties of point estimators, methods of finding estimators, confidence intervals and hypothesis testing, among others. The third part examines how the previous theory is applied in the linear regression model (which is the workhorse of econometrics), such as the simple linear regression model and derivation of the ordinary least squares (OLS) estimator, multiple linear regression and the matrix algebra form of least squares, properties of the OLS estimator and hypothesis testing, among others. This module is targeted at students who are interested in the theory side of statistics and econometrics.

By the end of the module students should be able to:

• review the theoretical foundations of mathematical statistics;
• apply statistical techniques to derive estimators, construct confidence intervals and test hypotheses;
• relate the statistical theory to the linear regression model;
• demonstrate the skills to prove theorems.