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Testing in nonparametric ANCOVA model based on ridit reliability functional

Author

Listed:
  • Debajit Chatterjee

    (Maulana Azad College)

  • Uttam Bandyopadhyay

    (University of Calcutta)

Abstract

In the spirit of Bross (Biometrics 14:18–38, 1958), this paper considers ridit reliability functionals to develop test procedures for the equality of $$K(>2)$$ K ( > 2 ) treatment effects in nonparametric analysis of covariance (ANCOVA) model with d covariates based on two different methods. The procedures are asymptotically distribution free and are not based on the assumption that the distribution functions (d.f.’s) of the response variable and the associated covariates are continuous. By means of simulation study, the proposed methods are compared with the methods provided by Tsangari and Akritas (J Multivar Anal 88:298–319, 2004) and Bathke and Brunner (Recent advances and trends in nonparametric statistics, Elsevier, Amsterdam, 2003) under ANCOVA in terms of type I error rate and power.

Suggested Citation

  • Debajit Chatterjee & Uttam Bandyopadhyay, 2019. "Testing in nonparametric ANCOVA model based on ridit reliability functional," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 71(2), pages 327-364, April.
    • Handle: RePEc:spr:aistmt:v:71:y:2019:i:2:d:10.1007_s10463-017-0643-8
    DOI: 10.1007/s10463-017-0643-8
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    References listed on IDEAS

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    1. Tsangari, Haritini & Akritas, Michael G., 2004. "Nonparametric ANCOVA with two and three covariates," Journal of Multivariate Analysis, Elsevier, vol. 88(2), pages 298-319, February.
    2. Wang, Lan & Akritas, Michael G., 2006. "Testing for Covariate Effects in the Fully Nonparametric Analysis of Covariance Model," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 722-736, June.
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    4. Matteo Grigoletto & Michael G. Akritas, 1999. "Analysis of Covariance with Incomplete Data Via Semiparametric Model Transformations," Biometrics, The International Biometric Society, vol. 55(4), pages 1177-1187, December.
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    6. Axel Munk & Natalie Neumeyer & Achim Scholz, 2007. "Non‐parametric Analysis of Covariance – The Case of Inhomogeneous and Heteroscedastic Noise," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 34(3), pages 511-534, September.
    7. Edgar Brunner & Frank Konietschke & Markus Pauly & Madan L. Puri, 2017. "Rank-based procedures in factorial designs: hypotheses about non-parametric treatment effects," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 79(5), pages 1463-1485, November.
    8. Daniel Fischer & Hannu Oja & Johanna Schleutker & Pranab K. Sen & Tiina Wahlfors, 2014. "Generalized Mann–Whitney Type Tests for Microarray Experiments," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 41(3), pages 672-692, September.
    9. Jan De Neve & Olivier Thas, 2015. "A Regression Framework for Rank Tests Based on the Probabilistic Index Model," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(511), pages 1276-1283, September.
    10. Michael G. Akritas & Ingrid Van Keilegom, 2001. "Non‐parametric Estimation of the Residual Distribution," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 28(3), pages 549-567, September.
    11. Edgar Brunner & Madan Puri, 2001. "Nonparametric methods in factorial designs," Statistical Papers, Springer, vol. 42(1), pages 1-52, January.
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