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Summary:
In the paper rank test statistics for testing the hypothesis of randomness are constructed for the case where only some observations are exactly measurable and the other ones are only known to lie in the intervals $(y_{j-1},y_j), \ 1\leq j\leq k, \ y_0< ... <y_k$. The observations lying in the same interval are treated as a tie in the case of noncontinuous distribution. The method of randomization and the method of averaged scores are used for the construction of linear statistics. The asymptotic normality of these statistics under the hypothesis and under contiguous alternatives is established.
References:
[1] Conover W. J.: Rank tests for one sample, two samples and k samples without the assumption of a continuous distribution function. Ann. Statist. 1 (1973), 1105-1125. DOI 10.1214/aos/1176342560 | MR 0350953 | Zbl 0275.62042
[2] Johnson R. A., Mehrotra K. G.: Locally most powerful rank tests for the two sample problem with censored data. Ann. Math. Statist. 43 (1972), 823 - 831. DOI 10.1214/aoms/1177692548 | MR 0314176 | Zbl 0246.62035
[3] Peto R., Peto J.: Asymptotically efficient rank invariant test procedures. J. Roy. Statist. Soc. Ser. A, 135 (1972), 185-206. DOI 10.2307/2344317
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