Second-order accurate inference on eigenvalues of covariance and correlation matrices

被引：7

作者：

Boik, RJ ^{[1
]}

机构：

[1] Montana State Univ, Dept Math Sci, Bozeman, MT 59717 USA

来源：

JOURNAL OF MULTIVARIATE ANALYSIS | 2005年 / 96卷 / 01期

关键词：

confidence interval; correlation matrix; covariance matrix; edgeworth expansion; eigenvalue; principal components analysis; saddlepoint approximation;

D O I：

10.1016/j.jmva.2004.09.009

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：

Edgeworth expansions and saddlepoint approximations for the distributions of estimators of certain eigenfunctions of covariance and correlation matrices are developed. These expansions depend on second-, third-, and fourth-order moments of the sample covariance matrix. Expressions for and estimators of these moments are obtained. The expansions and moment expressions are used to construct second-order accurate confidence intervals for the eigenfunctions. The expansions are illustrated and the results of a small simulation study that evaluates the finite-sample performance of the confidence intervals are reported. (c) 2004 Elsevier Inc. All rights reserved.

引用

页码：136 / 171

页数：36

共 50 条

[1] On the second-order statistics of the eigenvectors of sample covariance matrices
Friedlander, B
Weiss, AJ
IEEE TRANSACTIONS ON SIGNAL PROCESSING, 1998, 46 (11) : 3136 - 3139
[2] Second-Order Accurate Inference on Simple, Partial, and Multiple Correlations
Boik, Robert J.
Haaland, Ben
JOURNAL OF MODERN APPLIED STATISTICAL METHODS, 2006, 5 (02) : 283 - 308
[3] Covariance Matrices for Second-Order Vector Random Fields in Space and Time
Ma, Chunsheng
IEEE TRANSACTIONS ON SIGNAL PROCESSING, 2011, 59 (05) : 2160 - 2168
[4] Stability Analysis of a Class of Second-Order Switched Systems via Eigenvalues of Matrices
Muramatsu, Eiichi
2015 10TH ASIAN CONTROL CONFERENCE (ASCC), 2015,
[5] A method for calculating the eigenvalues of large Hermitian matrices by second-order recursion formulae
Mitsutake, A
Iitaka, T
Okamoto, Y
COMPUTER PHYSICS COMMUNICATIONS, 1996, 96 (2-3) : 217 - 231
[6] A general expression for second-order covariance matrices-an application to dispersion models
Magalhaes, Tiago M.
Botter, Denise A.
Sandoval, Monica C.
BRAZILIAN JOURNAL OF PROBABILITY AND STATISTICS, 2021, 35 (01) : 37 - 49
[7] On the second-order statistics of the sample covariance
Yu, NG
Xu, ZY
PIMRC 2003: 14TH IEEE 2003 INTERNATIONAL SYMPOSIUM ON PERSONAL, INDOOR AND MOBILE RADIO COMMUNICATIONS PROCEEDINGS, VOLS 1-3 2003, 2003, : 2953 - 2957
[8] The second-order derivatives of matrices of eigenvalues and eigenvectors with an application to generalized F-statistic
Dunajeva, O
LINEAR ALGEBRA AND ITS APPLICATIONS, 2004, 388 : 159 - 171
[9] On computing eigenvalues of second-order linear pencils
Annaby, M. H.
Tharwat, M. M.
IMA JOURNAL OF NUMERICAL ANALYSIS, 2007, 27 (02) : 366 - 380
[10] Inference in second-order identified models
Dovonon, Prosper
Hall, Alastair R.
Kleibergen, Frank
JOURNAL OF ECONOMETRICS, 2020, 218 (02) : 346 - 372

← 1 2 3 4 5 →