MAA304 - Asymptotic Statistics (2023-2024)

The course MAA304 begins with a detailed overview of convergence, both in probability and in distribution, and revisiting two key theorems in statistics: the law of large numbers and the central limit theorem. We will then look in detail at asymptotic statistics, including fundamental topics such as the asymptotic properties of maximum likelihood estimators (MLEs), the formulation of asymptotic confidence intervals, and the principles underlying asymptotic test theory.

We will then highlight the crucial role of information theory in statistics, with particular emphasis on notions of efficiency, Cramer-Rao theory, and sufficiency. Moving to multivariate linear regression, the focus shifts to inference in Gaussian models and model validation to give students a solid understanding of this important statistical paradigm.

Next, we turn to nonlinear regression and delve into a comprehensive study of logistic regression. The course concludes with a brief introduction to nonparametric statistics, emphasising the importance of distribution-free tests.

The course MAA304 begins with a detailed overview of convergence, both in probability and in distribution, and revisiting two key theorems in statistics: the law of large numbers and the central limit theorem. We will then look in detail at asymptotic statistics, including fundamental topics such as the asymptotic properties of maximum likelihood estimators (MLEs), the formulation of asymptotic confidence intervals, and the principles underlying asymptotic test theory.

We will then highlight the crucial role of information theory in statistics, with particular emphasis on notions of efficiency, Cramer-Rao theory, and sufficiency. Moving to multivariate linear regression, the focus shifts to inference in Gaussian models and model validation to give students a solid understanding of this important statistical paradigm.

Next, we turn to nonlinear regression and delve into a comprehensive study of logistic regression. The course concludes with a brief introduction to nonparametric statistics, emphasising the importance of distribution-free tests.