Please use this identifier to cite or link to this item: http://hdl.handle.net/11455/98128
標題: 具不完整資料的混合t因子分析器之最大概似推論
Maximum likelihood inference for mixtures of t factor analyzers with incomplete data
作者: 劉孟智
Meng-Chih Liu
關鍵字: 資料縮減;ECM 演算法;因子分析器;最大概似估計;多變量t分佈;遺失值;模型選擇;data reduction;ECM algorithms;factor analyzer;maximum likelihood estimation;multivariate t distribution;missing values;model selection
摘要: 
混合多變量t因子分析器(MtFA)已被廣泛地運用於穩健分群高維度且具厚尾雜訊的資料。然而,在配適MtFA模型時,遺失值的出現將使得分析相當棘手與計算過程繁複。在本篇論文,我們致力於發展一個快速的ECM演算法,在可能具有遺失值的MtFA模型中,能藉由用較少的資料擴增使其加速模型參數的最大概似估計。本文在考慮資料為隨機遺失的機制下,提出基於概似的推論。此外根據參數估計的大樣本理論,我們精確地推導模型的計分向量與經驗訊息矩陣。有關重建遺失值與分群部分觀察樣本的實際問題也將被探討。最後,我們透過模擬與實際資料分析來驗證我們所提出方法的實用性。

The mixtures of t factor analyzers (MtFA) is a powerful tool widely used for robust clustering of high-dimensional data in the presence of heavy-tailed noises. However, the occurrence of missing values may frequently cause analytical intractability and high computational complexity in the fitting of these models. In thesis, we aim at developing an expectation conditional maximization(ECM) algorithm with less data augmentation for fast maximum-likelihood (ML) estimation of MtFA with possibly missing values. For making likelihood-based inference, the missing data mechanism is considered to be missing at random (MAR). In addition, the score vector and empirical information matrix of the model are explicitly derived for large sample inference of estimated parameters. Practical issues related to the recovery of missing values and clustering of partially observed samples are also investigated. The practical utility of the proposed methodology is exemplified through the analysis of simulated and real data.
URI: http://hdl.handle.net/11455/98128
Rights: 同意授權瀏覽/列印電子全文服務,2021-08-20起公開。
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