Metrika

, Volume 29, Issue 1, pp 159–173 | Cite as

Local comparison of linear rank tests, in the Bahadur sense

  • E. Kremer
Article

Summary

As continuation ofKremer [1979a] a theory of asymptotic comparison based on local Bahadur efficiency is derived for general linear rank tests of the one-sample symmetry problem and thek-sample problem (k≥2). The results are similar to former considerations based on Pitman efficiency but hold under weaker conditions on the scores-generating functions or local alternatives.

Keywords

Stochastic Process Probability Theory Economic Theory Rank Test Weak Condition 

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References

  1. Bahadur, R.R.: Stochastic comparison of tests. Ann. Math. Statist.31, 1960, 276–295.Google Scholar
  2. —: Rates of convergence of estimates and test statistics. Ann. Math. Statist.38, 1967, 303–324.Google Scholar
  3. Bahadur, R.R., andM. Raghavachari: Some asymptotic properties of likelihood ratios on general sample spaces. Proc. 6. Berkeley Symp. on Math. Statist. Prob., 1972, 129–152.Google Scholar
  4. Behnen, K.: A characterization of certain rank-order tests with bounds for the asymptotic relative efficiency. Ann. Math. Statist.43, 1972, 1839–1851.Google Scholar
  5. Chernoff, H., andI.R. Savage: Asymptotic normality and efficiency of certain nonparametric test statistics. Ann. Math. Statist.29, 1958, 972–994.Google Scholar
  6. Groeneboom, P., andJ. Oosterhoff: Bahadur efficiency and probabilities of large deviations. Statistica neerlandica31, 1977, p. 1.Google Scholar
  7. Hájek, J.: Asymptotic sufficiency of the vector of ranks in the Bahadur sense. Ann. Statist.2, 1974, 75–83.Google Scholar
  8. Hájek, J., andZ. Šidák: Theory of rank tests. Prag-New York 1967.Google Scholar
  9. Ho, N.V.: Asymptotic efficiency in the Bahadur sense for signed rank tests. Proc. Praque Symp. Math. Statist. 1973, 127–156.Google Scholar
  10. Kremer, E.: Approximate and local Bahadur efficiency of linear rank tests in the two-sample problem. Ann. Statist.7, 1979a, 1246–1255.Google Scholar
  11. Kremer, E.: Lokale Bahadur-Effizienz linearer Rangtests. Doctoral dissertation, Universität Hamburg, 1979b.Google Scholar
  12. Kullback, S.: Information theory and statistics. New York 1959.Google Scholar
  13. Puri, M.L., andP.K. Sen: Nonparametric methods in multivariate analysis. New York 1971.Google Scholar
  14. Raghavachari, M.: On a theorem of Bahadur on the rate of convergence of test statistics. Ann. Math. Statist.41, 1970, 1695–1699.Google Scholar
  15. Ruymgaart, F.H.: Asymptotic theory of rank tests for independence. Math. Centre Tracts43, Amsterdam 1973.Google Scholar
  16. Ruymgaart, F.H., G.R. Shorack, andW.R. Van Zwet: Asymptotic normality of nonparametric tests for independence. Ann. Math. Statist.43, 1972, 1122–1135.Google Scholar
  17. Ruymgaart, F.H., andM.C.A. Van Zuilen: Asymptotic normality of multivariate linear rank statistics in the non-i.i.d. case. Ann. Statist.6, 1978, 588–602.Google Scholar
  18. Wieand, H.S.: A condition under which the Pitman and Bahadur approaches to efficiency coincide. Ann. Statist.4, 1976, 1003–1011.Google Scholar
  19. Woodworth, G.G.: Large deviations and Bahadur efficiency of linear rank statistics. Ann. Math. Statist.41, 1970, 251–283.Google Scholar

Copyright information

© Physica-Verlag 1982

Authors and Affiliations

  • E. Kremer
    • 1
  1. 1.Institut für Mathematische StochastikUniversität HamburgHamburg 13

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