Annals of the Institute of Statistical Mathematics

, Volume 18, Issue 1, pp 87–105

# On a class of c-sample weighted rank-sum tests for location and scale

• P. K. Sen
• Z. Govindarajulu
Article

## Summary

A class of c-sample (cε2) non-parametric tests for the homogeneity of location or scale parameters is proposed and their various properties studied. These tests are based on a family of congruent interquantile numbers, and may be regarded as the c-sample extension of a class of two sample tests, proposed and studied by Sen . A useful theorem on the asymptotic distribution of the proposed class of statistics is established. With the aid of this result, the asymptotic power-efficiency of the proposed class of test is studied and comparison is made with other test procedures. Location-free scale tests are also considered.

## Keywords

Asymptotic Normality Asymptotic Efficiency Scale Alternative Joint Probability Function Joint Characteristic Function
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## References

1. 
F. C. Andrews, “Asymptotic behaviour of some rank tests for analysis of variance,”Ann. Math. Statist., 25 (1954), 724–735.
2. 
V. P. Bhapkar, “A non-parametric test for the problem of several samples,”Ann. Math. Statist., 32 (1961), 1108–1117.
3. 
H. Chernoff and I. R. Savage, “Asymptotic normality and efficiency of certain nonparametric test statistics,”Ann. Math. Statist., 29 (1958), 972–994.
4. 
H. Cramér,Mathematical Methods of Statistics, Princeton University Press, 1946.Google Scholar
5. 
J. V. Deshpande, “A non-parametric test based on U-statistics for the problem of several samples,”Jour. Ind. Slat. Asso., 3 (1965), 20–29.
6. 
M. Dwass, “Some k-sample rank order tests,”Contributions to Probability and Statistics, Essays in honor of Harold Hotelling (Edited by I. Olkin et al) Stanford Univ. Press, 1960.Google Scholar
7. 
J. Kiefer, “K-sample analogues of the Kolmogorov-Smirnov and Cramer-Von Mises tests,”Ann. Math. Statist., 30 (1959), 420–447.
8. 
J. Klotz, “Non-parametric tests for scale,”Ann. Math. Statist., 33 (1962), 498–512.
9. 
W. H. Kruskal, “A non-parametric test for the several sample problem,”Ann. Math. Statist., 23 (1952), 525–540.
10. 
W. H. Kruskal and W. A. Wallis, “Use of ranks in one criterion analysis of variance,”Jour. Amer. Stat. Asso., 47 (1952), 583–621.
11. 
A. M. Mood,Introduction to the Theory of Statistics, McGraw Hill, New York, 1950.Google Scholar
12. 
M. L. Puri, “Asymptotic efficiency of a class of c-sample tests,”Ann. Math. Statist., 35 (1964), 102–121.
13. 
M. L. Puri, “On some tests of homogeneity of variances,”Tech. Report IMM-NYU 338, New York Univ. Courant Inst. Math. Sc., 1964.Google Scholar
14. 
P. K. Sen, “On the role of a class of quantile tests in some non-parametric problems,”Calcutta Stat. Assoc. Bull., 11 (1962), 125–143.
15. 
P. K. Sen, “On weighted rank-sum tests for dispersion,”Ann. Inst. Slat. Math., 15 (1963), 117–135.
16. 
P. K. Sen, “On stochastic convergence of sample extreme values from distributions with infinite end-points,”Jour. Ind. Soc. Agri. Stat., 16 (1964), 189–201.Google Scholar
17. 
E. Sverdrup, “The limit distribution of a continuous function of random variables,”Skandinavisk Aktuarietidskrift, 35 (1952), 1–10.
18. 
T. J. Terpestra, “A non-parametric k-sample test and its connection with II-test,” Report S(92) (VP2) ofStat. Dept. Math. Centre, Amsterdam, (1951).Google Scholar

© Institute of Statistical Mathematics 1966

## Authors and Affiliations

• P. K. Sen
• 1
• 2
• Z. Govindarajulu
• 1
• 2
1. 1.Calcutta UniversityIndia
2. 2.Case Institute of TechnologyUSA

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