Principal components selection given extensively many variables

被引：7

作者：

Lehmann, N ^{[1
]}

机构：

[1] Univ Duisburg Essen, Inst Med Informat Biometry & Epidemiol, D-45122 Essen, Germany

来源：

STATISTICS & PROBABILITY LETTERS | 2005年 / 74卷 / 01期

关键词：

principal components analysis; random matrix theory;

D O I：

10.1016/j.spl.2005.04.031

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

Principal components analysis relates to the eigenvalue distribution of Wishart matrices. Given few observations and very many variables this distribution maps to eigenvalue statistics in the Gaussian orthogonal ensemble. Principal components selection can then be based on existing analytical results. (c) 2005 Elsevier B.V. All rights reserved.

引用

页码：51 / 58

页数：8

共 16 条

[1] ASYMPTOTIC THEORY FOR PRINCIPAL COMPONENT ANALYSIS [J].

ANDERSON, TW .

ANNALS OF MATHEMATICAL STATISTICS, 1963, 34 (01) :122-&

[2]

[Anonymous], 1991, USERS GUIDE PRINCIPA

[3]

Bai ZD, 1998, ANN PROBAB, V26, P316

[4] Developments in random matrix theory [J].

Forrester, PJ ;

Snaith, NC ;

Verbaarschot, JJM .

JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 2003, 36 (12) :R1-R10

[5] An exact formula for general spectral correlation function of random Hermitian matrices [J].

Fyodorov, YV ;

Strahov, E .

JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 2003, 36 (12) :3203-3213

[6]

HAAKE R, 2000, QUANTUM SIGNATURE CH

[7] On the distribution of the largest eigenvalue in principal components analysis [J].

Johnstone, IM .

ANNALS OF STATISTICS, 2001, 29 (02) :295-327

[8] CHAOTIC SCATTERING - THE SUPERSYMMETRY METHOD FOR LARGE NUMBER OF CHANNELS [J].

LEHMANN, N ;

SAHER, D ;

SOKOLOV, VV ;

SOMMERS, HJ .

NUCLEAR PHYSICS A, 1995, 582 (1-2) :223-256

[9]

Marchenko V. A., 1967, MATH USSR SB, V114, P507, DOI [DOI 10.1070/SM1967V001N04ABEH001994, 10.1070/SM1967v001n04ABEH001994]

[10]

Mehta M L., 1991, Random Matrices

← 1 2 →