Some Tests Concerning the Covariance Matrix in High Dimensional Data

Muni S. Srivastava

Type: Article

Publication Date: 2005-01-01

Citations: 249

DOI: https://doi.org/10.14490/jjss.35.251

Abstract

In this paper, tests are developed for testing certain hypotheses on the covariance matrix Σ, when the sample size N = n + 1 is smaller than the dimension pof the data. Under the condition that (tr Σi⁄p) exists and > 0, as p → ∞, i =1,…,8, tests are developed for testing the hypotheses that the covariance matrix in a normally distributed data is an identity matrix, a constant time the identity matrix (spherecity), and is a diagonal matrix. The asymptotic null and non-null distributions of these test statistics are given.

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+	An Introduction to Multivariate Statistics	1993	David L. Streiner
+	The Limiting Distribution of Functions of Sample Means and Application to Testing Hypotheses	1983	P. L. Hsu
+ PDF Chat	Theory of multivariate statistics	2000	Martin Bilodeau David J. Brenner
+	Monotonicity of the modified likelihood ratio test for a covariance matrix	1967	Hisao Nagao
+	Monotonicity of the power functions of modified likelihood ratio criterion for the homogeneity of variances and of the sphericity test	1977	E.M. Carter Muni S. Srivastava
+	Some optimal multivariate tests	1971	S. John
+	Null distribution of the sum of squared z-transforms in testing complete independence	1990	Shande Chen Govind S. Mudholkar
+	Locally Best Invariant Test for Sphericity and the Limiting Distributions	1972	Nariaki Sugiura
+	On some test criteria for covariance matrix	1973	Hisao Nagao
+ PDF Chat	Some hypothesis tests for the covariance matrix when the dimension is large compared to the sample size	2002	Olivier Ledoit Michael Wolf