Mathematical Methods for Statistics and Econometrics (Solutions)

This module, Mathematical Methods for Statistics and Econometrics, examines the theoretical principles underpinning statistical methodology, with a focus on inferential techniques within parametric models. It is structured into three parts, beginning with core topics in probability theory, including counting methods, sample space and events, probability axioms, conditional probability, random variables, discrete and continuous distributions, multivariate distributions, and the central limit theorem. The second part focuses on estimation and inference, covering the properties of point estimators, methods for deriving estimators, confidence intervals, and hypothesis testing. The final part applies this theoretical foundation to econometrics, exploring the linear regression model. Topics include the simple and multiple linear regression models, derivation and properties of the ordinary least squares (OLS) estimator, the matrix algebra form of least squares, and hypothesis testing in regression analysis.

This module is tailored for students with an interest in the theoretical aspects of statistics and econometrics. By the end of the course, students will have a strong understanding of mathematical statistics, including the ability to derive estimators, construct confidence intervals, and test hypotheses. They will also develop the skills to connect statistical theory to econometric models, particularly the linear regression model, and demonstrate proficiency in proving key mathematical theorems related to these topics.