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Multivariate Behrens–Fisher problem with missing data

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  • Krishnamoorthy, K.
  • Yu, Jianqi

Abstract

Inference about the difference between two normal mean vectors when the covariance matrices are unknown and arbitrary is considered. Assuming that the incomplete data are of monotone pattern, a pivotal quantity, similar to the Hotelling T2 statistic, is proposed. A satisfactory moment approximation to the distribution of the pivotal quantity is derived. Hypothesis testing and confidence estimation based on the approximate distribution are outlined. The accuracy of the approximation is investigated using Monte Carlo simulation. Monte Carlo studies indicate that the approximate method is very satisfactory even for moderately small samples. The proposed methods are illustrated using an example.

Suggested Citation

  • Krishnamoorthy, K. & Yu, Jianqi, 2012. "Multivariate Behrens–Fisher problem with missing data," Journal of Multivariate Analysis, Elsevier, vol. 105(1), pages 141-150.
    • Handle: RePEc:eee:jmvana:v:105:y:2012:i:1:p:141-150
    DOI: 10.1016/j.jmva.2011.08.019
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    References listed on IDEAS

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    1. Yu, Jianqi & Krishnamoorthy, K. & Pannala, Maruthy K., 2006. "Two-sample inference for normal mean vectors based on monotone missing data," Journal of Multivariate Analysis, Elsevier, vol. 97(10), pages 2162-2176, November.
    2. Krishnamoorthy, K. & Yu, Jianqi, 2004. "Modified Nel and Van der Merwe test for the multivariate Behrens-Fisher problem," Statistics & Probability Letters, Elsevier, vol. 66(2), pages 161-169, January.
    3. 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. Konietschke, Frank & Bathke, Arne C. & Harrar, Solomon W. & Pauly, Markus, 2015. "Parametric and nonparametric bootstrap methods for general MANOVA," Journal of Multivariate Analysis, Elsevier, vol. 140(C), pages 291-301.
    2. 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.
    3. Xu, Li-Wen, 2015. "Parametric bootstrap approaches for two-way MANOVA with unequal cell sizes and unequal cell covariance matrices," Journal of Multivariate Analysis, Elsevier, vol. 133(C), pages 291-303.

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