Communications for Statistical Applications and Methods

  • 제25권1호
  • /
  • Pages.71-78
  • /
  • 2018
  • /
  • 2287-7843(pISSN)
  • /
  • 2383-4757(eISSN)
한국통계학회 (The Korean Statistical Society)
권호 표지
DOI QR코드

DOI QR Code

A note on the test for the covariance matrix under normality

  • 투고 : 2017.10.11
  • 심사 : 2017.12.05
  • 발행 : 2018.01.31
PDF 다운로드
⟨ 이전 논문 다음 논문 ⟩

초록

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.

키워드

참고문헌

  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. https://doi.org/10.1214/09-AOS694
  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. https://doi.org/10.1214/aos/1176346579
  3. Cai TT and Ma Z (2013). Optimal hypothesis testing for high dimensional covariance matrices, Bernoulli, 19, 2359-2388. https://doi.org/10.3150/12-BEJ455
  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. https://doi.org/10.1080/03610910801988987
  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. https://doi.org/10.1007/BF01844048
  7. Gupta AK and Bodnar T (2014). An exact test about the covariance matrix, Journal of Multivariate Analysis, 125, 176-189. https://doi.org/10.1016/j.jmva.2013.12.007
  8. Jolicoeur P and Mosimann JE (1960). Size and shape variation in the painted turtle: a principal component analysis, Growth, 24, 339-354.
  9. Kim J and Cheon S (2013). Bayesian multiple change-point estimation and segmentation, Communications for Statistical Applications and Methods, 20, 439-454. https://doi.org/10.5351/CSAM.2013.20.6.439
  10. Mardia KV, Kent JT, and Bibby JM (1979). Multivariate Analysis, Academic Press, New York.
  11. Park HI (2017). A simultaneous inference for the multivariate data, Journal of the Korean Data Analysis Society, 19, 557-564.
  12. Pinto LP and Mingoti SA (2015). On hypothesis tests for covariance matrices under multivariate normality, Pesquisa Operacional, 35, 123-142. https://doi.org/10.1590/0101-7438.2015.035.01.0123
  13. Silvey SD (1975). Statistical Inference, Chapman and Hall, London.