Statistical Modelling 11 (2011), 253277
Robust statistical modelling using the multivariate skew t distribution
with complete and incomplete data
Tsung-I Lin
Department of Applied Mathematics and Institute of Statistics,
National Chung Hsing University
Taichung
Taiwan
eMail: tilin@amath.nchu.edu.tw
Tzy-Chy Lin
Division of Clinical Science,
Center for Drug Evaluation
Taipei
Taiwan
Abstract:
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 expectation
conditional maximization 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;
MST model; multiple imputation; multivariate truncated t distribution
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