Bahadur efficiency of a test of exponentiality based on a loss-of-memory type functional equation

Journal of Nonparametric Statistics

Volumn 6, Issue 1, 1996, Pages 13-26

  Nikitin, Ya Yu ^a  

^a ST PETERSBURG STATE UNIVERSITY   (Russian Federation)

Author keywords

Bahadur slope; Consistency; Exponential distribution; Large deviations; Memoryless property; U statistics

Indexed keywords

EID: 0012492657     PISSN: 10485252     EISSN: None     Source Type: Journal    
DOI: 10.1080/10485259608832660     Document Type: Article

References (25)

1. Abbakumov, V. L., and Nikitin, Ya. Yu. (1993). Bahadur efficiency and local optimality of a new nonparametric test of symmetry, In: Statistics and probability, A R.R. Bahadur Festschrift, Wiley Eastern Ltd., New Delhi, pp. 1-12.
2. Abrahamson, I. G. (1967). Exact Bahadur efficiencies for the Kolmogorov-Smirnov and Kuiper one-and two-sample statistics, Ann. Math. Stat. 38, pp. 1475-1490.
3. Angus, J. E. (1982). Goodness-of-fit tests for exponentiality based on a loss-of-memory type functional equation, Journ. Statist. Plann. Inference 6, pp. 241-251.
4. Arnold, B. C. (1971). Two characterizations of the exponential distribution using order statistics, Unpublished manuscript, Iowa State University, Ames, Iowa.
5. Asher, S. (1990). A survey of tests of exponentiality, Commun. Statist. Theory and Meth. 19, pp. 1811-1825.
6. Bahadur, R. R. (1967). Rates of convergence of estimates and test statistics, Ann. Math. Statist., 38, pp. 303-324.
7. Bahadur, R. R. (1971). Some limit theorems in statistics, SIAM, Philadelphia.
8. Barlow, R. E., and F. Proschan. (1986). Inference for the exponential life distribution, In: Theory of Reliability, Proc. of the Internat. School of Physics "Enrico Fermi", North Holland, pp. 143-168.
9. Bergman, B., and Klefsjö, B. (1989). A family of test statistics for detecting monotone mean residual life, Journ. Statist. Plann. Inference, 21, pp.161-178.
10. Borovkov, A. A. (1986). Theory of Probability, Moscow, Nauka, (In Russian).
11. Dasgupta, R. (1984). On large deviation probabilities of U-statistics in non i.i.d. case, Sankhyā. Indian J. Statist, A46, pp. 110-116.
12. De Bruijn, N. G. (1958). Asymptotic methods in analysis, North-Holland, Amsterdam.
13. Demyanov, V. F., and Malozemov, V. N. (1990). Introduction to Minimax, Dover Publ., Inc., NY.
14. Deshpande, J. V. (1983). A class of tests for exponentiality against increasing failure rate average alternatives, Biometrika, 70, pp. 514-518.
15. Doksum, K. A., and Yandell, B. S. (1984). Test for exponentiality, In: Handbook of Statistics, P. R. Krishnaiah and P. K. Sen (eds), North Holland, 4, pp. 579-611.
16. Gradshteyn, I. S., and Ryzhik, I. M. (1971). Tables of Integrals, Sums, Series and Products, 5th ed., Nauka, Moscow.
17. Groeneboom, P., and Shorack, G. (1981). Large deviations of goodness-of-fit statistics and linear combinations of order statistics, Ann. Probab. 9, pp. 971-987.
18. Gupta, R. C. (1973). A characteristic property of the exponential distribution, Sankhyā, B35, pp. 365-366.
19. Koul, H. L. (1977). A test for new better than used, Commun. Statist. Theory Meth. A6, pp. 563-574.
20. Nikitin, Ya. Yu. (1984). Bahadur local asymptotic optimality and characterization problems, Theory Probab. Applic. 29, pp. 79-92.
21. Nikitin, Ya. Yu. (1995). Asymptotic efficiency of nonparametric tests, Cambridge University Press.
22. Raghavachari, M. (1970). On a theorem of Bahadur on the rate of convergence of test statistics, Ann. Math. Stat., 41, pp. 1695-1699.
23. Sinha, B. K., and Wieand, H. S. (1977). Bounds on the efficiencies of four commonly used nonparametric tests of location, Sankhyā, B39, pp. 121-129.
24. Spurrier, J. D. (1984). An overview of tests for exponentiality, Commun. Statist. Theory Meth. 13, pp. 1635-1654.
25. Stephens, M. A. (1986). Tests for exponential distribution, In: Goodness-of-Fit Techniques, Birkhäuser, New York-Basel, pp. 421-459.