Analysis of Multivariate Skew Normal Models with Incomplete Data
碩士 === 國立中興大學 === 應用數學系所 === 96 === In this paper, we establish computationally flexible methods and algorithms for the analysis of multivariate skew normal (MSN) models when missing values occur in the data. To facilitate the computation and simplify the derivations of theoretic results, we introdu...
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| Format: | Others |
| Language: | en_US |
| Online Access: | http://ndltd.ncl.edu.tw/handle/22402169053296302522 |
| Summary: | 碩士 === 國立中興大學 === 應用數學系所 === 96 === In this paper, we establish computationally flexible methods and algorithms for the analysis of multivariate skew normal (MSN) models when missing values occur in the data. To facilitate the computation and simplify the derivations of theoretic results, we introduce two auxiliary indicator matrices into the model for the determination of observed and missing components of each observation. Under missing at random (MAR) mechanisms, we present an analytically simple EM algorithm for computing parameter estimates and performing a single imputation for each missing value. For multiple imputations of missing data, an efficient data augmentation (DA) scheme using the Gibbs sampler is developed to conduct Bayesian inference. The proposed methodologies are illustrated through a real data set and comparisons are made with those obtained from fitting the normal counterparts.
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