scholarly journals On testing homogeneity of two covariance matrices with nonnormal data

2019 ◽  
Vol 1324 ◽  
pp. 012102
Author(s):  
Jieqiong Shen ◽  
Junyan Li
Keyword(s):  
Covariance Matrices ◽  
Nonnormal Data ◽  
Testing Homogeneity

Testing homogeneity of high-dimensional covariance matrices

2019 ◽  
Author(s):  
Shurong Zheng ◽  
Ruitao Lin ◽  
Jianhua Guo ◽  
Guosheng Yin
Keyword(s):  
Covariance Matrices ◽  
High Dimensional ◽  
Testing Homogeneity

scholarly journals NONNULL DISTRIBUTION OF LRC FOR TESTING HOMOGENEITY OF COVARIANCE MATRICES OF COMPLETELY SYMMETRIC GAUSSIAN MODELS

1991 ◽  
Vol 22 (1) ◽  
pp. 13-24
Author(s):  
A. K. GUPTA ◽  
D. K. NAGAR ◽  
VIPIN TAYAL
Keyword(s):  
Asymptotic Distribution ◽  
Likelihood Ratio ◽  
Hypergeometric Functions ◽  
Likelihood Ratio Statistic ◽  
Covariance Matrices ◽  
Zonal Polynomials ◽  
Gaussian Models ◽  
Testing Homogeneity ◽  
Nonnull Distribution

The nonnull moments of the likelihood ratio statistic for testing equality of covariance matrices of completely symmetric Gaussian models are obta.ined in terms of the Lauricella's hypergeometric functions and also in terms of zonal polynomials. Then the nonnull asymptotic distribution of the statistic is derived under certain alternatives for unequal samples.

Quadratic Discriminant Analysis of Spatially Correlated Data

2001 ◽  
Vol 6 (2) ◽  
pp. 15-28 ◽  
Author(s):  
K. Dučinskas ◽  
J. Šaltytė
Keyword(s):  
Discriminant Function ◽  
Error Rate ◽  
Gaussian Random Field ◽  
Correlated Data ◽  
Covariance Matrices ◽  
Classification Rule ◽  
Spatial Correlations ◽  
Linear Quadratic ◽  
Spatial Correlation Function ◽  
Spatially Correlated

The problem of classification of the realisation of the stationary univariate Gaussian random field into one of two populations with different means and different factorised covariance matrices is considered. In such a case optimal classification rule in the sense of minimum probability of misclassification is associated with non-linear (quadratic) discriminant function. Unknown means and the covariance matrices of the feature vector components are estimated from spatially correlated training samples using the maximum likelihood approach and assuming spatial correlations to be known. Explicit formula of Bayes error rate and the first-order asymptotic expansion of the expected error rate associated with quadratic plug-in discriminant function are presented. A set of numerical calculations for the spherical spatial correlation function is performed and two different spatial sampling designs are compared.

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