Robust Statistical Modelling Using the Multivariate Skew t Distribution with Complete and Incomplete Data
Tsung-I. Lin1, Tzy-Chy Lin2
1Institute of Statistics, National Chung Hsing University, Taichung, Taiwan; 2Taiwan FDA

Missing data is inevitable in many situations that could hamper data analysis for scientific investigations. We establish flexible analytical tools for multivariate skew t models when fat-tailed, asymmetric and missing observations simultaneously occur in the input data. For the ease of computation and theoretical developments, two auxiliary indicator matrices are incorporated into the model for the determination of observed and missing components of each observation that can effectively reduce the computational complexity. Under the missing at random assumption, we present a Monte Carlo version of the ECM algorithm, which is performed to estimate the parameters and retrieve each missing observation with a single value. Additionally, a Metropolis-Hastings within Gibbs sampler with data augmentation is developed to account for the uncertainty of parameters as well as missing outcomes. The methodology is illustrated through two real data sets.

Keywords: Data augmentation; MCECM algorithm; Missing at random; Multivariate truncated t distribution

Biography: Tsung-I Lin is at a full Professor in the Department of Applied Mathematics and the Institute of Statistics at National Chung Hsing University, Taiwan. He received his B.A. in Applied Mathematics from National Chung Hsing University, Taiwan in 1993, the M.S. in Statistics from National Tsing Hua University, Hsinchu, Taiwan in 1997 and Ph.D. in Statistics from National Chiao Tung University, Hsinchu, Taiwan in 2003. His research interest focuses on multivariate analysis, financial statistics, computational statistics and Bayesian analysis.