SELECTION PROCEDURES TO SELECT POPULATIONS BETTER THAN A CONTROL

  • Kumar, Narinder (Department of Statistics, Panjab University) ;
  • Khamnel, H.J. (Department of Statistics, Tabriz University)
  • Published : 2003.06.01

Abstract

In this paper, we propose two selection procedures for selecting populations better than a control population. The bestness is defined in terms of location parameter. One of the procedures is based on two-sample linear rank statistics whereas the other one is based on a comparatively simple statistic, and is useful when testing time is expensive so that an early termination of an experiment is desirable. The proposed selection procedures are seen to be strongly monotone. Performance of the proposed procedures is assessed through simulation study.

Keywords

References

  1. Annals of the Institute of Statistical Matheamtics v.20 Some distribution free statistics and their application to the selection problem Bartlett,N.S.;Govindarajulu,Z. https://doi.org/10.1007/BF02911626
  2. CHAKRABORTI, S. AND DESU, M. M. (1989). 'A class of distribution free tests for testing homogeneity against ordered alternatives', Statistics & Probability Letters, 6, 251-256 https://doi.org/10.1016/0167-7152(88)90070-3
  3. DAVID, H. A. (1981). Order Statistics, 2nd ed., John Wiley and Sons
  4. DESHPANDE, J. V. AND MEHTA, G. P. (1983). 'Non-parametric procedures to select popula-tions better than a known standard', Sankhya, B45, 330-334
  5. GUPTA, S. S. AND NAGEL, K. (1971). 'On some contributions to multiple decision theory and related topics', In Statistical Decision Theory and Related Topics (S. S. Gupta and J. Yackel, eds.), 79-102, Academic Press, New York
  6. GUPTA, S. S., NAGEL, K. AND PANCHAPAKESAN, S. (1973). 'On the order statistics from equally correlated normal variables', Biometrika, 60, 403-413 https://doi.org/10.1093/biomet/60.2.403
  7. GILL, A. N. AND MEHTA, G. P. (1993). 'Selecting populations better than the control : Scale parameter case', Statistics & Decisions, 11, 251-271
  8. HSU, J. C. (1980). 'Robust and non-parametric subset selection procedures', Communications in Statistics-Theory and Methods, A9, 1439-1459
  9. HSU, J. C. (1981). 'A class of non-parametric subset selection procedures', Sankhya, B43, 235-244
  10. KOZIOL, J. A. AND REID, N. (1977). 'On the asymptotic equivalence of two ranking methods for k-sample linear rank statistics', The Annals of Statistics, 5, 1099-1106 https://doi.org/10.1214/aos/1176343998
  11. LANN, P. VANDER (1991a). 'The efficiency of subset selection of an almost best treatment' COSOR-Memoranda, 19, Eindhoven University of Technology, Eindhoven
  12. LANN, P. VANDER.(1991b). 'Subset selection of an e-best population : Efficiency results', COSOR-Memoranda, 19, Eindhoven University of Technology, Eindhoven
  13. LANN, P. VANDER (1992). 'Subset selection of an almost best treatment', BiometricaI JournaI, 34, 647-656 https://doi.org/10.1002/bimj.4710340602
  14. LEHMANN, E. L. (1963). 'A class of selection procedures based on ranks', Mathematicsche Annalen, 150, 268-275 https://doi.org/10.1007/BF01396995
  15. MAHAMUNULA, D. M. (1967). .'Some fixed-sample ranking and selection problems', The AnnaIs of MathematicaI Statistics, 38, 1079-1091 https://doi.org/10.1214/aoms/1177698778
  16. PURI, P. S. AND PURl, M. L. (1968). 'Selection procedures based on ranks : Scale parameter case', Sankhya, A30, 291-302
  17. PURI, P. S. AND PURl, M. L. (1969). 'Multiple decision procedures based on ranks for certain problems in analysis of variance', The AnnaIs of Mathematical Statistics, 40, 619-632 https://doi.org/10.1214/aoms/1177697730
  18. RIZVI, M. H., SOBEL, M. AND WOODWORTH, G. G. (1968). 'Non-parametric ranking proce-dures for comparison with a control', The Annals of Mathematical Statistics, 39, 2075-2093 https://doi.org/10.1214/aoms/1177698035
  19. RIZVI, M. H. AND WOODWORTH, G. G. (1970). 'On selection procedures based on ranks: counter examples concerning least favourable configurations', The Annals of Mathemat-ical Statistics, 41, 1942-1951 https://doi.org/10.1214/aoms/1177696695
  20. SANTNER, T. J. (1975). 'A restricted subset selection approach to ranking and selection procedures', The AnnaIs of Statistics, 3, 334-339 https://doi.org/10.1214/aos/1176343060