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Inferences on a Normal Covariance Matrix and Generalized Variance with Monotone Missing Data

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  • Hao, Jian
  • Krishnamoorthy, K.

Abstract

The problems of testing a normal covariance matrix and an interval estimation of generalized variance when the data are missing from subsets of components are considered. The likelihood ratio test statistic for testing the covariance matrix is equal to a specified matrix, and its asymptotic null distribution is derived when the data matrix is of a monotone pattern. The validity of the asymptotic null distribution and power analysis are performed using simulation. The problem of testing the normal mean vector and a covariance matrix equal to a given vector and matrix is also addressed. Further, an approximate confidence interval for the generalized variance is given. Numerical studies show that the proposed interval estimation procedure is satisfactory even for small samples. The results are illustrated using simulated data.

Suggested Citation

  • Hao, Jian & Krishnamoorthy, K., 2001. "Inferences on a Normal Covariance Matrix and Generalized Variance with Monotone Missing Data," Journal of Multivariate Analysis, Elsevier, vol. 78(1), pages 62-82, July.
    • Handle: RePEc:eee:jmvana:v:78:y:2001:i:1:p:62-82
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    References listed on IDEAS

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    1. Fujikoshi, Yasunori, 1985. "Selection of variables in two-group discriminant analysis by error rate and Akaike's information criteria," Journal of Multivariate Analysis, Elsevier, vol. 17(1), pages 27-37, August.
    2. K. Krishnamoorthy & Maruthy Pannala, 1998. "Some Simple Test Procedures for Normal Mean Vector with Incomplete Data," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 50(3), pages 531-542, September.
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    Cited by:

    1. Tomoya Yamada & Megan Romer & Donald Richards, 2015. "Kurtosis tests for multivariate normality with monotone incomplete data," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 24(3), pages 532-557, September.
    2. Krishnamoorthy, K., 2013. "Comparison of confidence intervals for correlation coefficients based on incomplete monotone samples and those based on listwise deletion," Journal of Multivariate Analysis, Elsevier, vol. 114(C), pages 378-388.
    3. Abdelhamid Hassairi & Fatma Ktari & Raoudha Zine, 2022. "On the Gaussian representation of the Riesz probability distribution on symmetric matrices," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 106(4), pages 609-632, December.
    4. Nobumichi Shutoh & Takahiro Nishiyama & Masashi Hyodo, 2017. "Bartlett correction to the likelihood ratio test for MCAR with two-step monotone sample," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 71(3), pages 184-199, August.
    5. Chang, Wan-Ying & Richards, Donald St.P., 2009. "Finite-sample inference with monotone incomplete multivariate normal data, I," Journal of Multivariate Analysis, Elsevier, vol. 100(9), pages 1883-1899, October.
    6. Yin, Yanqing, 2021. "Test for high-dimensional mean vector under missing observations," Journal of Multivariate Analysis, Elsevier, vol. 186(C).
    7. Tsukada, Shin-ichi, 2014. "Equivalence testing of mean vector and covariance matrix for multi-populations under a two-step monotone incomplete sample," Journal of Multivariate Analysis, Elsevier, vol. 132(C), pages 183-196.
    8. Batsidis, A. & Zografos, K. & Loukas, S., 2006. "Errors in discrimination with monotone missing data from multivariate normal populations," Computational Statistics & Data Analysis, Elsevier, vol. 50(10), pages 2600-2634, June.
    9. Richards, Donald St. P. & Yamada, Tomoya, 2010. "The Stein phenomenon for monotone incomplete multivariate normal data," Journal of Multivariate Analysis, Elsevier, vol. 101(3), pages 657-678, March.
    10. Tsukada, Shin-ichi, 2014. "Asymptotic expansion for distribution of the trace of a covariance matrix under a two-step monotone incomplete sample," Journal of Multivariate Analysis, Elsevier, vol. 129(C), pages 206-219.
    11. Chang, Wan-Ying & Richards, Donald St. P., 2010. "Finite-sample inference with monotone incomplete multivariate normal data, II," Journal of Multivariate Analysis, Elsevier, vol. 101(3), pages 603-620, March.
    12. Kurita, Eri & Seo, Takashi, 2022. "Multivariate normality test based on kurtosis with two-step monotone missing data," Journal of Multivariate Analysis, Elsevier, vol. 188(C).

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