Zhou, Xian; Jammalamadaka, S. Rao Bahadur efficiencies of spacings tests for goodness of fit. (English) Zbl 0698.62049 Ann. Inst. Stat. Math. 41, No. 3, 541-553 (1989). Summary: This paper is concerned with the exact Bahadur efficiencies of spacing statistics. For a general class of statistics based on a fixed number of spacings, the explicit forms of the exact slopes are derived, and it is shown that the sum of the logarithms of spacings is optimal in this class. Some results are extended to the case where the number of spacings increase with the sample size to infinity. Cited in 10 Documents MSC: 62G10 Nonparametric hypothesis testing 60F10 Large deviations 62G20 Asymptotic properties of nonparametric inference 62G30 Order statistics; empirical distribution functions Keywords:goodness of fit; Dirichlet distributions; exact Bahadur efficiencies of spacing statistics; fixed number of spacings; explicit forms of the exact slopes; sum of the logarithms of spacings PDFBibTeX XMLCite \textit{X. Zhou} and \textit{S. R. Jammalamadaka}, Ann. Inst. Stat. Math. 41, No. 3, 541--553 (1989; Zbl 0698.62049) Full Text: DOI References: [1] Bahadur, R. R. (1960). Stochastic comparison of tests,Ann. Math. Statist.,31, 276-295. · Zbl 0201.52203 · doi:10.1214/aoms/1177705894 [2] Del, Pino, G. E. (1979). On the asymptotic distribution ofk-spacings with applications to goodness of fit tests,Ann. Statist.,7, 1058-1065. · Zbl 0425.62026 · doi:10.1214/aos/1176344789 [3] Hoeffding, W. (1965). Asymptotically optimal tests for multinomial distributions,Ann. Math. Statist.,36, 369-408. · Zbl 0135.19706 · doi:10.1214/aoms/1177700150 [4] Jammalamadaka, S. R. and Tiwari, R. C. (1987). Efficiencies of some disjoint spacings tests relative to a chi-square test,New Perspectives in Theoretical and Applied Statistics, (eds. M. L., Puri, J., Wilaplana and W., Wertz), 311-318, Wiley, New York. · Zbl 0655.62053 [5] Jammalamadaka, S. R., Zhou, X. and Tiwari, R. C. (1986). Asymptotic efficiencies of spacings tests for goodness of fit, Tech. Report No. 4, Statistics Program, UCSB. · Zbl 0702.62041 [6] Kuo, M. and Rao, J. S. (1981). Limit theory and efficiencies for tests based on higher order spacings,Statistics?Applications and New Directions, Proceedings of the Golden Jubilee Conference of the Indian Statistical Institute, 333-352, Statistical Publishing Society, Calcutta. [7] Quine, M. P. and Robinson, J. (1985). Efficiencies of chi-square and likelihood ratio goodness-of-fit tests,Ann. Statist.,13, 795-802. · Zbl 0576.62061 · doi:10.1214/aos/1176349550 [8] Rao, J. S. and Kuo, M. (1984). Asymptotic results on the Greenwood statistic and some of its generalizations,J. Roy. Statist. Soc. Ser. B,46, 228-237. · Zbl 0554.62040 [9] Sethuraman, J. and Rao, J. S. (1970). Pitman efficiencies of tests based on spacings,Nonparametric Techniques in Statistical Inference, 405-416, Cambridge Univ. Press, Cambridge. This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.