Department of Mathematics - Seminar on Statistics - A class of new symmetric distributions based on scale mixtures of normal distribution and mean regression models by using N-EM and US algorithms

In this paper, we propose a class of new symmetric distributions as candidates or alternatives to model continuous data on the real line, when existing distributions (such as normal, Student's t, two-parameter Laplace, logistic and so on) perform the data-fitting not well enough. Motivated by the stochastic representation (SR) of the random variable (r.v.) following Student's t-distribution, the authors study the general mixture of normal (Ge-N) distribution, which is defined by an SR involving a normal r.v. with zero mean and a positive r.v. with an arbitrary distribution. The Ge-N distribution includes the commonly-used t, two-parameter Laplace, logistic distributions as three special cases and possesses a clear statistical interpretation. In the Ge-N framework, we first address the issue of identifiability of parameters, then develop three specific scale mixtures of normal distribution and corresponding mean regression models for analyzing continuous data with covariates. We apply the normalized expectation-maximization (N-EM) algorithm aided by the upper-crossing/solution (US) algorithm to calculate maximum likelihood estimates of parameters. Simulation studies on model comparisons showed that the proposed three new models extend the application scope of existing models. Two real data sets are analyzed to illustrate the proposed methods.
[This is a joint work with Mr. Yuefan WU, Mr. Yuanfan ZHAO, Prof. Zudi LU, Prof. Hua ZHOU, Dr. Xun-Jian LI]