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Two-sample inference for normal mean vectors based on monotone missing data

Author

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  • Yu, Jianqi
  • Krishnamoorthy, K.
  • Pannala, Maruthy K.

Abstract

Inferential procedures for the difference between two multivariate normal mean vectors based on incomplete data matrices with different monotone patterns are developed. Assuming that the population covariance matrices are equal, a pivotal quantity, similar to the Hotelling T2 statistic, is proposed, and its approximate distribution is derived. Hypothesis testing and confidence estimation of the difference between the mean vectors based on the approximate distribution are outlined. The validity of the approximation is investigated using Monte Carlo simulation. Monte Carlo studies indicate that the approximate method is very satisfactory even for small samples. A multiple comparison procedure is outlined and the proposed methods are illustrated using an example.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:jmvana:v:97:y:2006:i:10:p:2162-2176
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    References listed on IDEAS

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    1. 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. Yin, Yanqing, 2021. "Test for high-dimensional mean vector under missing observations," Journal of Multivariate Analysis, Elsevier, vol. 186(C).
    2. Tsukada, Shin-ichi, 2024. "Hypothesis testing for mean vector and covariance matrix of multi-populations under a two-step monotone incomplete sample in large sample and dimension," Journal of Multivariate Analysis, Elsevier, vol. 202(C).
    3. Shutoh, Nobumichi & Hyodo, Masashi & Seo, Takashi, 2011. "An asymptotic approximation for EPMC in linear discriminant analysis based on two-step monotone missing samples," Journal of Multivariate Analysis, Elsevier, vol. 102(2), pages 252-263, February.
    4. 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.
    5. Mizuki Onozawa & Ayaka Yagi & Takashi Seo, 2020. "New Test Statistics for One and Two Mean Vectors with Two-step Monotone Missing Data," International Journal of Statistics and Probability, Canadian Center of Science and Education, vol. 9(6), pages 1-56, November.
    6. Krishnamoorthy, K. & Yu, Jianqi, 2012. "Multivariate Behrens–Fisher problem with missing data," Journal of Multivariate Analysis, Elsevier, vol. 105(1), pages 141-150.

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