STATS 730 consists of interactive lectures covering classical and advanced aspects of statistical inference and individually assigned research projects to be presented in class. The lecture component consists in an introduction to simple maximum likelihood concepts is followed by a discussion of point estimators, including methods to find them and key properties such as mean squared error, sufficiency, ancillarity, and unbiasedness. (Asymptotic efficiency is also discussed in the second half of the course.) The Halmos-Savage, Rao-Blackwell and Cramér-Rao theorem are discussed and applied. This segment is followed by an in-depth consideration of the likelihood-based frequentist approach to inference. Simple and not-so-simple (e.g., finite mixture model) examples based on independent and identically distributed samples are presented. The essential properties, concepts and tools of maximum-likelihood inference are then presented, with an equal focus on theory, such as asymptotic evaluations, and on applications. Maximum likelihood and extensions are applied in a wide variety of settings with examples in R, with special attention to exponential families applied to generalised linear modelling. The course concludes by looking at extensions of maximum likelihood for models for more challenging situations, including quasi-likelihood and conditional likelihood.
The research component consists in an assigned project to be completed in two phases, based on an assigned topic, a research question and a given data set: 1) a literature review and description of the methods to be applied to answer the research question using the data; 2) the results of the analysis. Each phase will be presented by the students, and be the object of an assessed in-class quiz co-created by the presenting students and the instructors. The topics involved will be varied and current, some of them taken from methods for dependent data, survival analysis, methods to handle missing data, predictive analytics, causal inference, semi-parametric inference, and others.
Prior familiarity with R is strongly advised for those undertaking this course.