Designs Robust Against Presence of an Outlier in an Analysis of Covariance Model

Abstract

Presence of one or more aberration in the observations affects inference procedure in statistical analysis. Block designs robust against presence of aberrations can be found in the literature for both regression and block design set-ups. In this paper, an attempt has been made to find robust designs in a block design set-up with covariates, when there is one single wild observation in the study variable. Specifically, effects on the estimation of a full set of orthonormal treatment contrasts and that on the estimation of covariate parameters have been considered.

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References

  1. Biswas A (2012) Block designs robust against the presence of an aberration in a treatment control set up. Commun Stat Theory Methods 41:920–933

    Article  Google Scholar 

  2. Biswas A, Das P, Mandal NK (2015) Designs robust against violation of normality assumption in the standard F-test. Commun Stat Theory Methods 44:2898–2910

    MathSciNet  Article  Google Scholar 

  3. Box GEP, Draper NR (1975) Robust designs. Biometrika 62:347–352

    MathSciNet  Article  Google Scholar 

  4. Das K, Mandal NK, Sinha BK (2003) Optimal experimental designs for models with covariates. J Stat Plan Inference 115:273–285

    MathSciNet  Article  Google Scholar 

  5. Das P, Dutta G, Mandal NK, Sinha BK (2015) Optimal covariate designs-theory and applications. Springer, Berlin

    Google Scholar 

  6. Dutta G, Das P, Mandal NK (2009) Optimum covariate designs in partially balanced incomplete block (PBIB) design set ups. J Stat Plan Inference 139:2823–2835

    MathSciNet  Article  Google Scholar 

  7. Dutta G, Das P, Mandal NK (2010a) Optimum covariate designs in binary proper equi-replicate block design set up. Discrete Math 310:1037–1049

    MathSciNet  Article  Google Scholar 

  8. Ghosh S, Roy J (1982) Optimality in presence of damaged observations. J Stat Plann Inference 6:123–126

    MathSciNet  Article  Google Scholar 

  9. Gopalan R, Dey A (1976) On robust experimental designs. Sankhyā 38(B):297–299

    MathSciNet  MATH  Google Scholar 

  10. Harville DA (1975) Computing optimum designs for covariate models. In: Srivastava JN (ed) A Survey of statistical design and linear models. Amsterdam, North Holland, pp 209–228

    Google Scholar 

  11. Lopes Troya J (1982a) Optimal designs for covariate models. J Stat Plan Inference 6:373–419

    MathSciNet  Article  Google Scholar 

  12. Lopes Troya J (1982b) Cyclic designs for a covariate model. J Stat Plan Inference 7:49–75

    MathSciNet  Article  Google Scholar 

  13. Mandal NK (1989) On robust designs. Calcutta Stat Assoc Bull 38:115–119

    MathSciNet  Article  Google Scholar 

  14. Mandal NK, Shah KR (1993) Designs robust against aberrations. Calcutta Stat Assoc Bull 43:95–107

    MathSciNet  Article  Google Scholar 

  15. Rao CR (1973) Linear statistical inference and its applications. Wiley, New York

    Google Scholar 

  16. Sarkar S, Gupta VK, Parsad R (2003) Robust block designs for making test treatments-control treatment comparisons against the presence of an outlier. J Ind Soc Agric Stat 56:7–18

    MathSciNet  MATH  Google Scholar 

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Acknowledgements

The authors acknowledge the anonymous referee for suggestions and valuable comments.

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Correspondence to Ganesh Dutta.

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Dutta, G., Mandal, N.K. & Das, P. Designs Robust Against Presence of an Outlier in an Analysis of Covariance Model. J Indian Soc Probab Stat (2020). https://doi.org/10.1007/s41096-020-00084-w

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Keywords

  • Block design
  • Covariates
  • Outlier
  • Robust design

Mathematics Subject Classification

  • 62K25