报 告 人：吴启宏 教授
报告题目：How good is the first order asymptotic normality of MLE？
报告时间：
报告地点：静远楼1506学术报告厅
报告摘要：During the last global financial crisis, many commentators and researchers have blamed the usual Gaussian assumption of the statistical models. Even if this underlying assumption is replaced, we are still going to use the first-order asymptotic normality of maximum likelihood estimators (MLE), the so-called “delta method.” Since there is no theoretical guideline on sample size needed in applications, the applied researchers (and even the journal referees) seem to act as if there is no requirement on sample size at all. In this talk, I shall demonstrate on spot by means of SAS software that the asymptotic normality can be far off the theoretical mark even in usually unsuspected scenarios. This might be explained by the basic fact that any non-linear transform of a normal random variable (or vector) cannot lead to a normal variable (or vector). That is, the convergence to normal distribution as the sample size tends to infinity cannot be a uniform convergence over the family of all non-linear one-to-one transforms. So for any particular large sample size there cannot be more than one in the family that can be well-approximated by a normal distribution. And thus it is sheer luck that the one falls on our hands without transformation is the one.
吴启宏教授简介：
吴启宏(Kai Wang Ng)教授是香港大学统计及精算系前系主任，名誉教授。美国统计学会会员，英国皇家统计学会Follow，泛华统计协会终身会员，香港统计学会终身会员。现为“Insurance: Mathematics and Economic”和“Case Studies in Business, Industry and Government Statistics”等杂志副主编。研究领域包括 Foundation of inference. Converse of Bayes' Theorem and applications. Distribution theory. Actuarial & financial risk. Applications of asymptotic theory. Multivariate analysis. Linear models. Data mining & Informatics.