Maximum Likelihood Inference for Mixtures of Common t-Factor Analyzers with Missing Information
碩士 === 逢甲大學 === 統計學系統計與精算碩士班 === 102 === Mixture of common factor analyzers (MCFA), which is a fusion of Gaussian mixture models and factor analysis models, provides the ability to analyze high-dimensional data from a heterogeneous population. The model considerably reduces the number of parameters...
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ndltd-TW-102FCU053360092015-10-13T23:49:49Z http://ndltd.ncl.edu.tw/handle/10295397996199341827 Maximum Likelihood Inference for Mixtures of Common t-Factor Analyzers with Missing Information 具遺失訊息混合共同t 因子分析器 之最大概似推論 Jyong-Nan Yang 楊烱男 碩士 逢甲大學 統計學系統計與精算碩士班 102 Mixture of common factor analyzers (MCFA), which is a fusion of Gaussian mixture models and factor analysis models, provides the ability to analyze high-dimensional data from a heterogeneous population. The model considerably reduces the number of parameters in the specification of component-covariance matrices through factor-analytic representation of the component-covariance matrices and common component-factor loadings. For the data with clusters of having nonnormality or heavy tails, a robust extension of MCFA, called the mixture of common t-factor analyzers (MCtFA), has become a more flexible approach due to less than ideal sensitivity to outliers. Unfortunately, the existing MCtFA model does not allow to handle missing values that frequently occur in many scientific investigations. The thesis accommodates the analysts with a general framework for fitting the MCtFA with incomplete data. To carry out maximum likelihood estimation of the model parameters, we develop an efficient ECME and AECM algorithm under a missing at random mechanism. A visualization tool for clustering, a classification rule for allocating new individuals, a diagnostic guideline for outliers, and an imputation method for filling in missing data under the proposed approach are also provided.Illustrative examples are presented to describe the usefulness of our methodology and compare the finite sample performance of various competing models. Wan-Lun Wang 王婉倫 2014 學位論文 ; thesis 71 zh-TW |
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碩士 === 逢甲大學 === 統計學系統計與精算碩士班 === 102 === Mixture of common factor analyzers (MCFA), which is a fusion of Gaussian mixture models and factor analysis models, provides the ability to analyze high-dimensional data from a heterogeneous population. The model considerably reduces the number of parameters in the specification of component-covariance matrices through factor-analytic representation of the component-covariance matrices and common component-factor loadings. For the data with clusters of having nonnormality or heavy tails, a robust extension of MCFA, called the mixture of common t-factor analyzers (MCtFA), has become a more flexible approach due to less than ideal sensitivity to outliers. Unfortunately, the existing MCtFA model does not allow to handle missing values that frequently occur in many scientific investigations. The thesis accommodates the analysts with a general framework for fitting the MCtFA with incomplete data. To carry out maximum likelihood estimation of the model parameters, we develop an efficient ECME and AECM algorithm under a missing at random mechanism. A visualization tool for clustering, a classification rule for allocating new individuals, a diagnostic guideline for outliers, and an imputation method for filling in missing data under the proposed approach are also provided.Illustrative examples are presented to describe the usefulness of our methodology and compare the finite sample performance of various competing models.
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author2 |
Wan-Lun Wang |
author_facet |
Wan-Lun Wang Jyong-Nan Yang 楊烱男 |
author |
Jyong-Nan Yang 楊烱男 |
spellingShingle |
Jyong-Nan Yang 楊烱男 Maximum Likelihood Inference for Mixtures of Common t-Factor Analyzers with Missing Information |
author_sort |
Jyong-Nan Yang |
title |
Maximum Likelihood Inference for Mixtures of Common t-Factor Analyzers with Missing Information |
title_short |
Maximum Likelihood Inference for Mixtures of Common t-Factor Analyzers with Missing Information |
title_full |
Maximum Likelihood Inference for Mixtures of Common t-Factor Analyzers with Missing Information |
title_fullStr |
Maximum Likelihood Inference for Mixtures of Common t-Factor Analyzers with Missing Information |
title_full_unstemmed |
Maximum Likelihood Inference for Mixtures of Common t-Factor Analyzers with Missing Information |
title_sort |
maximum likelihood inference for mixtures of common t-factor analyzers with missing information |
publishDate |
2014 |
url |
http://ndltd.ncl.edu.tw/handle/10295397996199341827 |
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