Browse > Article
http://dx.doi.org/10.29220/CSAM.2018.25.1.071

A note on the test for the covariance matrix under normality  

Park, Hyo-Il (Department of Statistics, Cheongju University)
Publication Information
Communications for Statistical Applications and Methods / v.25, no.1, 2018 , pp. 71-78 More about this Journal
Abstract
In this study, we consider the likelihood ratio test for the covariance matrix of the multivariate normal data. For this, we propose a method for obtaining null distributions of the likelihood ratio statistics by the Monte-Carlo approach when it is difficult to derive the exact null distributions theoretically. Then we compare the performance and precision of distributions obtained by the asymptotic normality and the Monte-Carlo method for the likelihood ratio test through a simulation study. Finally we discuss some interesting features related to the likelihood ratio test for the covariance matrix and the Monte-Carlo method for obtaining null distributions for the likelihood ratio statistics.
Keywords
asymptotic normality; likelihood ratio test; Monte-Carlo method; multivariate data;
Citations & Related Records
Times Cited By KSCI : 1  (Citation Analysis)
연도 인용수 순위
1 Bai Z, Jiang D, Yao JF, and Zheng S (2009). Corrections to LRT on large-dimensional covariance matrix by RMT, The Annals of Statistics, 37, 3822-3840.   DOI
2 Beran R and Srivastava MS (1985). Bootstrap tests and confidence regions for functions of a covariance matrix, The Annals of Statistics, 13, 95-115.   DOI
3 Cai TT and Ma Z (2013). Optimal hypothesis testing for high dimensional covariance matrices, Bernoulli, 19, 2359-2388.   DOI
4 Costa AFB and Machado MAG (2008). A new chart for monitoring the covariance matrix of bivariate processes, Communications in Statistics - Simulation and Computation, 37, 1453-1465.   DOI
5 Chung KL (2001). A Course in Probability Theory (3rd ed), Academic Press, New York.
6 Frets GP (1921). Heredity of headform in man, Genetica, 3, 193-384.   DOI
7 Gupta AK and Bodnar T (2014). An exact test about the covariance matrix, Journal of Multivariate Analysis, 125, 176-189.   DOI
8 Jolicoeur P and Mosimann JE (1960). Size and shape variation in the painted turtle: a principal component analysis, Growth, 24, 339-354.
9 Park HI (2017). A simultaneous inference for the multivariate data, Journal of the Korean Data Analysis Society, 19, 557-564.
10 Mardia KV, Kent JT, and Bibby JM (1979). Multivariate Analysis, Academic Press, New York.
11 Pinto LP and Mingoti SA (2015). On hypothesis tests for covariance matrices under multivariate normality, Pesquisa Operacional, 35, 123-142.   DOI
12 Silvey SD (1975). Statistical Inference, Chapman and Hall, London.
13 Kim J and Cheon S (2013). Bayesian multiple change-point estimation and segmentation, Communications for Statistical Applications and Methods, 20, 439-454.   DOI