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Title: Rank test of hypothesis of randomness against a group of regression alternatives (English)
Author: Nguyen, van Huu
Language: English
Journal: Aplikace matematiky
ISSN: 0373-6725
Volume: 17
Issue: 6
Year: 1972
Pages: 422-447
Summary lang: English
Summary lang: Czech
Category: math
Summary: The problem of testing hypothesis of randomness against a group of alternatives of regression in a parameter is investigated and a rank test for this problem is suggested. This problem is a generalization of the problem of detecting a shift in a location parameter of a distribution occurring at an unknown time point between consecutively taken observations. The rank test in this work is shown to be locally average most powerful within the class of all possible rank tests in the sense of the definition in Section §3. The asymptotic normality of the rank test statistic and the asymptotic efficiency of the rank test are shown not only for the case of location and scale parameter but for the case of general parameter. ()
MSC: 62G10
idZBL: Zbl 0258.62025
idMR: MR0315837
DOI: 10.21136/AM.1972.103435
Date available: 2008-05-20T17:54:39Z
Last updated: 2020-07-28
Stable URL:
Reference: [1] G. K. Bhattacharyya R. A. Johnson: Nonparametric tests for shift at unknown time point.Annals of Math. Stat. 39 (1968) No. 5, 1731-1743. MR 0230425, 10.1214/aoms/1177698156
Reference: [2] H. Chernoff S. Zacks: Estimating the current mean of a normal distribution which is subjected to changes in time.Annals of Math. Stat. 35 (1964), 999-1018. MR 0179874, 10.1214/aoms/1177700517
Reference: [3] J. Hájek Z. Šidák: Theory of rank tests.Academia, Publishing house of the Czechoslovak Academy of Sciences, Praha 1967. MR 0229351
Reference: [4] M. Hušková: Asymptotic distribution of simple linear rank statistics used for testing symmetry hypotheses.(Czech.) Thesis, Prague 1968.
Reference: [5] M. Hušková: Asymptotic distribution of simple linear rank statistic for testing of symmetry.Z. Wahrscheinlichkeitstheorie. Geb. 14, (1970), 308-322. MR 0277050, 10.1007/BF00533668
Reference: [6] Z. Kander S. Zacks: Test procedure for possible changes in parameters of statistical distribution occurring at unknown time point.Annals of Math. Stat. 37(1966), 1196-1210. MR 0202242, 10.1214/aoms/1177699265
Reference: [7] E. L. Lehmann: Testing statistical hypotheses.J. Wiley, New York, 1959. Zbl 0089.14102, MR 0107933
Reference: [8] E. L. Lehmann: Some concepts of independence.Annals of Math. Stat. 37 (1966) No. 2, 1137-1153. MR 0202228, 10.1214/aoms/1177699260
Reference: [9] E. S. Page: Continuous inspection schemes.Biometrika 41 (1954), 100-116. Zbl 0056.38002, MR 0088850, 10.1093/biomet/41.1-2.100
Reference: [10] E. S. Page: A test for a change in parameter occurring at an unknown point.Biometrika 42 (1955), 523-526. MR 0072412, 10.1093/biomet/42.3-4.523


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