Previous |  Up |  Next

Article

Summary:
The paper concerns the problem of testing the hypothesis of randomness against a group of regression alternatives combined with a subsequent decision which of the alternatives is true. A rank decision rule for this problem is proposed which is locally optimal. For some special cases also the asymptotic distributions of the testing statistics are studied.
References:
[1] Doob J. L.: Heuristic approach to the Kolmogorov - Smirnov theorem. Annals of Math. Stat. 20 (1949), 393-403. DOI 10.1214/aoms/1177729991
[2] Hájek J., Šidák Z.: Theory of Rank Tests. Academia, Publishing House of the Czechoslovak Academy of Sciences. Praha 1967. MR 0229351
[3] Hall I. J., Kudo A.: On slippage tests I. A generalization of Neyman-Pearson's Lemma. Annals of Math. Stat. 39 (1968), 1693-1699. Zbl 0182.51401
[4] Hall I. J., Kudo A., Yeh N.C.: On slippage tests II. Similar slippage tests. Annals of Math. Stat. 39 (1968), 2029-2037. DOI 10.1214/aoms/1177698030 | Zbl 0176.48601
[5] Karlin S., Truax D. R.: Slippage problems. Annals of Math. Stat. 31 (1960), 296-324. DOI 10.1214/aoms/1177705895 | Zbl 0131.35602
[6] Mosteller F.: A k-sample slippage test for an extreme population. Annals of Math. Stat. 19 (1948), 53-65. DOI 10.1214/aoms/1177730290 | Zbl 0031.37102
[7] Nguyen van Huu: Rank test of hypothesis of randomness against a group of regression alternatives. Aplikace Matematiky 17 (1972), 422-447. MR 0315837 | Zbl 0258.62025
[8] Paulson E.: An optimal solution to k-sample slippage problem for the normal distribution. Annals of Math. Stat. 23 (1952), 610-616, DOI 10.1214/aoms/1177729340 | MR 0052077
[9] Pfanzagl J.: Ein kombiniertes Test & Klassifikations-Problem. Metrika 2 (1959), 11-45. MR 0102149
[10] Slepian D.: The one-sided barrier problem for Gaussian noise. Bell System Techn. J. 41 (1962), 463-501. DOI 10.1002/j.1538-7305.1962.tb02419.x | MR 0133183
[11] Truax D. R.: An optimum slippage test for the variance of k normal distributions. Annals of Math. Stat. 24 (1953) 669-674. DOI 10.1214/aoms/1177728923 | MR 0060784
Partner of
EuDML logo