Grant: Discovery Grants Program - Individual

The focus of my research is asymptotics (the expansion of a statistic or a distribution) to gain a deeper understanding of mathematical statistics and probability theory. My research incorporates the statistical inference for the cross-product ratio, Yule's Q, and the ratio and other parametric functions of binomial proportions as the main components for studying their asymptotic behaviour. The long term goal of my research program is to advance statistical inference procedures by applying asymptotic analysis to develop novel approaches for solving a variety of problems in mathematical statistics. The two long-term objectives toward achieving this goal are investigations of consistency of model selection approaches for statistical learning methods, and statistical inference of parametric functions of binomial proportions. In the short term, focus will be on analyzing different types of consistencies of statistical learning techniques, and statistical inference for parametric functions of binomial proportions. This research is important because it will allow us a better understanding of the resulting applications, especially in quality control and biostatistics, which are important for industry and researchers. Moreover, it contributes to the development of the mathematical statistics and probability theory, which is of interest to statisticians and practitioners of statistics. The expected outcomes of this research include: a) the training of new, highly qualified personnel, especially those from underrepresented groups of Indigenous, female, and minority populations, who will be strongly equipped in the field of statistics and its applications; and, b) the advancement of knowledge in the field of mathematical statistics and probability, both of which are studied and applied globally by statisticians, biologists, epidemiologists, and practitioners in industry who focus on quality control.