主 题：Generating function based statistical inference for multivariate distributions
主讲人：Prof. Ong Seng Huat
主办单位：统计研究中心 统计学院 科研处
Prof Ong’s research areas include Discrete distributions, especially mixture models, analysis of count data, special functions and applications, data mining and statistical analysis of data and Applied Stochastic Modelling, times series of counts. He have published nearly 80 papers in many SCI journals, such as JMVA, Metrika. He is the associate editors of two journals: Malaysian Journal of Science, Sankhya B. He was the Elected member of ISI, International Statistical Institute (2001) and the Fellow of Academy of Sciences Malaysia (2010). He won the Award For Excellence in Service, University of Malaya with six number and the Malaysian Toray Science Foundation Science and Technology Award with one time.
Maximum likelihood (ML) estimation is a popular method for parameter estimation in statistical modelling due to its desirable properties. It is well-known that ML estimation is sensitive to outliers and alternative robust estimation methods like minimum Hellinger distance (MHD) have been used researchers and practitioners. However, in the multivariate setting, ML and MHD methods are computationally intensive since the joint probability density function (pdf) of the model is usually complicated. In this presentation, the probability (moment) generating function is proposed as a tool for quick and robust parameter estimation and goodness-of-fit. The rationale is that in many statistical models, the generating function has a much simpler form compared to the pdf. The proposed method is shown to perform well for simulated and real data, and is computationally much faster than ML or MHD estimation. Consistency and asymptotic normality of the estimators will be discussed. The proposed method is illustrated with a bivariate and a five-variate negative binomial distributions. If time permits, the formulation of these distributions which is of independent interest will also be briefly discussed.