Abstract
Let Xij j= 1,2,…,ni. be a random sample of size ni. from an absolutely continuous distribution with distributionfunction F(×/σi.), with mean O; i = 1,2,…,k. The problem considered is to test the null hypothesis HO: σ1. = σ2 = … = σk, against the alternative H1.: σ ≤ σ2 ≤ ≤ ≤ πk, Let 2 ≤ c.d ≤ min(n1, n2, …, nk, ) be two fixed integers and let ø(Xi1.…, Xic, Xj1, …, Xjd, ) take value 1 (−1) when max as well as min of (Xi1., …,Xic, Xj1, …, Xjd, ) are both Xj.’s (Xi, s) and it takes a value zero, otherwise. Let Ui,j. be the U-statistic corresponding to the kernel øij. The proposed test statistic is Wc,d, = with large values of Wc,d, leading to rejection of HO. The optimum values of ai’s are obtained. The tests are quite efficient.
AMS 1980 subject classifications: Primary 62G10; Secondary 62G20.
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© 1986 Springer-Verlag Berlin Heidelberg
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Kochar, S.C., Gupta, R.P. (1986). A Class of Distribution-Free Tests for Testing Homogeneity of Variances Against Ordered Alternatives. In: Dykstra, R., Robertson, T., Wright, F.T. (eds) Advances in Order Restricted Statistical Inference. Lecture Notes in Statistics, vol 37. Springer, New York, NY. https://doi.org/10.1007/978-1-4613-9940-7_9
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DOI: https://doi.org/10.1007/978-1-4613-9940-7_9
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