期刊
COMMUNICATIONS IN STATISTICS-SIMULATION AND COMPUTATION
卷 52, 期 5, 页码 1962-1978出版社
TAYLOR & FRANCIS INC
DOI: 10.1080/03610918.2021.1894336
关键词
Bijective function; Cramé r-von Mises test; Distribution function; Goodness-of-fit test; Kernel smoothing; Kolmogorov-Smirnov test; Transformation
This article proposes kernel-type smoothed Kolmogorov-Smirnov and Cramer-von Mises tests for data on general interval using bijective transformations, aiming to solve the boundary problem. Numerical studies are conducted to illustrate the performance of the estimator and the tests.
We propose kernel-type smoothed Kolmogorov-Smirnov and Cramer-von Mises tests for data on general interval, using bijective transformations. Though not as severe as in the kernel density estimation, utilizing naive kernel method directly to those particular tests will result in boundary problem as well. This happens mostly because the value of the naive kernel distribution function estimator is still larger than 0 (or less than 1) when it is evaluated at the boundary points. This situation can increase the errors of the tests especially the second-type error. In this article, we use bijective transformations to eliminate the boundary problem. Some numerical studies illustrating the estimator and the tests' performances will be presented in the last part of this article.
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