Previous |  Up |  Next


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.
[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
[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. DOI 10.1214/aoms/1177700517 | MR 0179874
[3] J. Hájek Z. Šidák: Theory of rank tests. Academia, Publishing house of the Czechoslovak Academy of Sciences, Praha 1967. MR 0229351
[4] M. Hušková: Asymptotic distribution of simple linear rank statistics used for testing symmetry hypotheses. (Czech.) Thesis, Prague 1968.
[5] M. Hušková: Asymptotic distribution of simple linear rank statistic for testing of symmetry. Z. Wahrscheinlichkeitstheorie. Geb. 14, (1970), 308-322. DOI 10.1007/BF00533668 | MR 0277050
[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. DOI 10.1214/aoms/1177699265 | MR 0202242
[7] E. L. Lehmann: Testing statistical hypotheses. J. Wiley, New York, 1959. MR 0107933 | Zbl 0089.14102
[8] E. L. Lehmann: Some concepts of independence. Annals of Math. Stat. 37 (1966) No. 2, 1137-1153. DOI 10.1214/aoms/1177699260 | MR 0202228
[9] E. S. Page: Continuous inspection schemes. Biometrika 41 (1954), 100-116. DOI 10.1093/biomet/41.1-2.100 | MR 0088850 | Zbl 0056.38002
[10] E. S. Page: A test for a change in parameter occurring at an unknown point. Biometrika 42 (1955), 523-526. DOI 10.1093/biomet/42.3-4.523 | MR 0072412
Partner of
EuDML logo