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Ranking procedures for matched pairs with missing data — Asymptotic theory and a small sample approximation

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  • Konietschke, F.
  • Harrar, S.W.
  • Lange, K.
  • Brunner, E.

Abstract

Nonparametric methods for matched pairs with data missing completely at random are considered. It is not assumed that the observations are coming from distribution functions belonging to a certain parametric or semi-parametric family. In particular, the distributions can have different shapes under the null hypothesis. Hence, the so-called nonparametric Behrens–Fisher problem for matched pairs with missing data is considered. Moreover, a new approach for confidence intervals for nonparametric effects is presented. In particular, no restriction on the ratio of the number of complete and incomplete cases is required to derive the asymptotic results. Simulations show that for arbitrary settings of complete data and missing values, the resulting confidence intervals maintain the pre-assigned coverage probability quite accurately. Regarding the power, none of the proposed tests is uniformly superior to the other. A real data set illustrates the application.

Suggested Citation

  • Konietschke, F. & Harrar, S.W. & Lange, K. & Brunner, E., 2012. "Ranking procedures for matched pairs with missing data — Asymptotic theory and a small sample approximation," Computational Statistics & Data Analysis, Elsevier, vol. 56(5), pages 1090-1102.
    • Handle: RePEc:eee:csdana:v:56:y:2012:i:5:p:1090-1102
    DOI: 10.1016/j.csda.2011.03.022
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    References listed on IDEAS

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    1. Akritas, Michael G. & Antoniou, Efi S. & Kuha, Jouni, 2006. "Nonparametric Analysis of Factorial Designs With Random Missingness: Bivariate Data," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 1513-1526, December.
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    4. Yan Lin & Stuart Lipsitz & Debajyoti Sinha & Atul A. Gawande & Scott E. Regenbogen & Caprice C. Greenberg, 2009. "Using Bayesian p‐values in a 2 × 2 table of matched pairs with incompletely classified data," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 58(2), pages 237-246, May.
    5. U. Munzel, 1999. "Nonparametric methods for paired samples," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 53(3), pages 277-286, November.
    6. Bernard Rosner & Robert J. Glynn & Mei-Ling T. Lee, 2006. "Extension of the Rank Sum Test for Clustered Data: Two-Group Comparisons with Group Membership Defined at the Subunit Level," Biometrics, The International Biometric Society, vol. 62(4), pages 1251-1259, December.
    7. Michael G. Akritas & Jouni Kuha & D. Wayne Osgood, 2002. "A Nonparametric Approach to Matched Pairs with Missing Data," Sociological Methods & Research, , vol. 30(3), pages 425-454, February.
    8. Munzel, Ullrich, 1999. "Linear rank score statistics when ties are present," Statistics & Probability Letters, Elsevier, vol. 41(4), pages 389-395, February.
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    Cited by:

    1. Li, Huiqiong & Tian, Guoliang & Tang, Niansheng & Cao, Hongyuan, 2018. "Assessing non-inferiority for incomplete paired-data under non-ignorable missing mechanism," Computational Statistics & Data Analysis, Elsevier, vol. 127(C), pages 69-81.
    2. Burim Ramosaj & Markus Pauly, 2019. "Predicting missing values: a comparative study on non-parametric approaches for imputation," Computational Statistics, Springer, vol. 34(4), pages 1741-1764, December.
    3. Hani M. Samawi & Robert Vogel, 2014. "Notes on two sample tests for partially correlated (paired) data," Journal of Applied Statistics, Taylor & Francis Journals, vol. 41(1), pages 109-117, January.
    4. Harrar, Solomon W. & Feyasa, Merga B. & Wencheko, Eshetu, 2020. "Nonparametric procedures for partially paired data in two groups," Computational Statistics & Data Analysis, Elsevier, vol. 144(C).
    5. Daniel Gaigall, 2020. "Testing marginal homogeneity of a continuous bivariate distribution with possibly incomplete paired data," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 83(4), pages 437-465, May.

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