A test of goodness-of-fit based on extreme spacings with some efficiency comparisons. (English) Zbl 0638.62038

Tests for the goodness-of-fit problem based on sample spacings, i.e., observed distances between successive order statistics, have been used in the literature. We propose a new test based on the number of “small” and “large” spacings. The asymptotic theory under close alternative sequences is also given thus enabling one to calculate the asymptotic relative efficiencies of such tests. A comparison of the new test and other spacings tests is given.


62G10 Nonparametric hypothesis testing
62E20 Asymptotic distribution theory in statistics
62G30 Order statistics; empirical distribution functions
62E15 Exact distribution theory in statistics
62G20 Asymptotic properties of nonparametric inference
Full Text: DOI EuDML


[1] Darling DA (1953) On a class of problems related to the random division of an interval. Ann Math Stat 24:239–253 · Zbl 0053.09902
[2] Darling DA (1962) Correction to ”On a class of problems related to the random division of an interval. Ann Math Stat 33:812
[3] Fraser DAS (1957) Nonparametric methods in statistics. John Wiley, New York · Zbl 0077.12903
[4] Puri ML, Rao JS, Yoon Y (1979) A simple test for goodness of fit based on spacings with some efficiency comparisons. In: Jureckov√° J (ed) Contributions to statistics. Academia, Prague, pp 197–209 · Zbl 0418.62035
[5] Pyke R (1965) Spacings. J Roy Stat Soc B 27:395–449
[6] Rao JS, Sethuraman J (1975) Weak convergence of the empirical distribution function of random variables subject to perturbations and scale factors. Ann Stat 3:299–313 · Zbl 0306.62007
[7] Sethuraman J, Rao JS (1970) Pitman efficiencies of tests based on spacings. In: Puri ML (ed) Nonparametric techniques in statistical inference. Cambridge University Press, pp 405–415
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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.