论文标题
一般间隔数据的无边界内核平滑拟合测试测试
Boundary-free Kernel-smoothed Goodness-of-fit Tests for Data on General Interval
论文作者
论文摘要
我们提出内核型使用bioxtive Transformations在一般间隔上平滑了Kolmogorov-Smirnov和Cramér-von Mises测试。尽管不像内核密度估计中那样严重，但直接利用天真的内核方法来进行这些特定测试也会导致边界问题。这主要是因为在边界点进行评估时，天真内核分布函数估计器的值仍大于$ 0 $（或小于$ 1 $）。这种情况可能会增加测试的错误，尤其是第二类误差。在本文中，我们使用徒使用徒转换来消除边界问题。一些仿真结果说明了估计器和测试的性能，将在本文的最后一部分中介绍。
We propose kernel-type smoothed Kolmogorov-Smirnov and Cramér-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 simulation results illustrating the estimator and the tests' performances will be presented in the last part of this article.
