樣本共變異數矩陣特徵值之中央極限定理

Chu-Chi Lee; 李竺祈

請用此 Handle URI 來引用此文件： http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/60299

完整後設資料紀錄

DC 欄位	值	語言
dc.contributor.advisor	張志中
dc.contributor.author	Chu-Chi Lee	en
dc.contributor.author	李竺祈	zh_TW
dc.date.accessioned	2021-06-16T10:15:05Z	-
dc.date.available	2013-09-02
dc.date.copyright	2013-09-02
dc.date.issued	2013
dc.date.submitted	2013-08-19
dc.identifier.citation	[1] Zhidong Bai and Jack W. Silverstein. Spectral analysis of large dimensional random matrices. Springer series in statistics. Springer, 2nd ed edition, 2010. [2] V. I. Bogachev. Gaussian measures. Number 62 in Mathematical surveys and monographs. American Mathematical Society, 2nd ed edition, 1998. [3] A. Lytova and L. Pastur. Central limit theorem for linear eigenvalue statistics of random matrices with independent entries. The Annals of Probability, 37(5): 1778 – 1840, 2009. [4] V. Marchenko and L. Pastur. The eigenvalue distribution in some ensembles of random matrices. Math. USSR Sbornik 1, pages 457–483, 1967. [5] Y. V. Prokhorov and Y. A. Rozanov. Probability Theory. Springer, 1969. [6] E. C. Titchmarsh. Introduction to the theory of fourier integrals. Oxford University Press, 2nd ed edition, 1948. 57
dc.identifier.uri	http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/60299	-
dc.description.abstract	在這篇文章中，我們補充了許多[3] 省略的細節，完整的證明樣本共變數矩陣特徵值的中央極限定理。	zh_TW
dc.description.abstract	In this paper, we provide the details omitted in [3] and give complete proofs on the central limit theorems for linear eigenvalue statistics of sample covariance matrices.	en
dc.description.provenance	Made available in DSpace on 2021-06-16T10:15:05Z (GMT). No. of bitstreams: 1 ntu-102-R99221038-1.pdf: 341110 bytes, checksum: 82cda9f81f78665f60faef22210cb041 (MD5) Previous issue date: 2013	en
dc.description.tableofcontents	致謝3 中文摘要7 Abstract 9 1 Introduction 11 1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 1.2 Notation and results . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 1.3 Preliminaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 2 Central limit theorem for linear eigenvalue statistics of the Wishart ensemble 19 2.1 Generalities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 2.2 Limiting normalized counting measure of eigenvalues . . . . . . . . . 21 2.3 Central limit theorem for linear eigenvalue statistics . . . . . . . . . . 24 3 Central limit theorem for linear eigenvalue statistics of sample covariance matrices: the case of zero excess of entries 33 3.1 Generalities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 3.2 Limiting normalized counting measure of eigenvalues . . . . . . . . . 35 3.3 Central limit theorem for linear eigenvalue statistics . . . . . . . . . . 38 4 Central limit theorem for linear eigenvalue statistics of sample covariance matrices in the general case 45 4.1 Variance estimates . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 4.2 Central limit theorem for linear eigenvalue statistics . . . . . . . . . . 47
dc.language.iso	en
dc.subject	特徵值	zh_TW
dc.subject	中央極限定理	zh_TW
dc.subject	樣本共變數矩陣	zh_TW
dc.subject	Sample covariance matrices	en
dc.subject	Linear eigeinvalue statistics	en
dc.subject	Central limit theorem	en
dc.title	樣本共變異數矩陣特徵值之中央極限定理	zh_TW
dc.title	On the Central Limit Theorem for Linear Eigenvalue Statistics of Sample Covariance Matrices	en
dc.type	Thesis
dc.date.schoolyear	101-2
dc.description.degree	碩士
dc.contributor.oralexamcommittee	陳宏,黃啟瑞
dc.subject.keyword	樣本共變數矩陣,特徵值,中央極限定理,	zh_TW
dc.subject.keyword	Sample covariance matrices,Linear eigeinvalue statistics,Central limit theorem,	en
dc.relation.page	57
dc.rights.note	有償授權
dc.date.accepted	2013-08-19
dc.contributor.author-college	理學院	zh_TW
dc.contributor.author-dept	數學研究所	zh_TW
顯示於系所單位：	數學系

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