Randomized rejection procedure for the two-sample Kolmogorov–Smirnov statistic
- 作者：Greenwell ; Raymond N. ; Finch ; Stephen J.
- 关键词：Kolmogorov&ndash ; Smirnov ; Continuity correction ; Discretization ; Randomization
- 刊名：Computational Statistics and Data Analysis
- 出版年：2004
- 期刊代码：19_01679473
- 类别：cp
- 出版时间：June 1, 2004
- 卷：46
- 期：2
- 页码：257-267
- 文件大小：222 K
摘要
The two-sample Kolmogorov–Smirnov test is unable to achieve an arbitrary probability of Type I error because it can only take on a limited number of discrete values. We offer a randomized procedure that achieves any specified value of α. We derive formulas for approximating the achievable p-values immediately above and below the desired value of α. For the value of the statistic corresponding to the p-value greater than α, our procedure rejects the null hypothesis randomly with probability sufficient to achieve the specified α. Such a procedure is particularly appropriate for simulation studies. Our procedure leads to a different continuity correction than the one proposed by Kim (J. Amer. Statist. Assoc. 64 (1969) 1625), using the criterion that the continuity correction should cause the randomized procedure to reject the null hypothesis with probability α.