高維度環境下Kronecker包絡主成分分析的漸近性;On the asymptotics of the Kronecker envelope principal component analysis in high-dimensional settings

Please use this identifier to cite or link to this item: http://ir.lib.ncu.edu.tw/handle/987654321/95276

Title:	高維度環境下Kronecker包絡主成分分析的漸近性;On the asymptotics of the Kronecker envelope principal component analysis in high-dimensional settings
Authors:	林祥曆;Lin, Siang-Li
Contributors:	統計研究所
Keywords:	漸近常態性;維度縮減;高維度小樣本;Kronecker包絡;主成分分析
Date:	2024-07-10
Issue Date:	2024-10-09 16:37:10 (UTC+8)
Publisher:	國立中央大學
Abstract:	主成分分析（PCA）是一種廣泛運用於資料預處理步驟中的降維方法，但在低信噪比的高維資料分析中，PCA的性能可能受到限制。為了解決這個問題，先前的研究提出了Kronecker包絡主成分分析（KEPCA）可作為PCA的替代方法。在本文中，我們介紹了Wang et al.(2024)在高維度理論中提出的KEPCA的一致性和漸近常態性，同時，我們經由模擬實驗和實際資料分析將其與經典PCA進行比較，逕而驗證了理論結果。 ;Principal Component Analysis (PCA) is a widely used dimension reduction method in data preprocessing, but its performance may be limited in the analysis of high-dimensional data with low signal-to-noise ratios. To address this issue, previous research proposed Kronecker Envelope Principal Component Analysis (KEPCA) as an alternative to PCA. In this article, we introduce the consistency and asymptotic normality of KEPCA, which is proposed by Wang et al.(2024) and we compare it with classical PCA through simulation experiments and real data analysis.
Appears in Collections:	[Graduate Institute of Statistics] Electronic Thesis & Dissertation

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