论文标题
均匀分布对分布函数凹入性测试的最不受欢迎的性能
Least favorability of the uniform distribution for tests of the concavity of a distribution function
论文作者
论文摘要
对单位间隔中包含的支持的分布函数的凹入性的测试可以基于根据经验分布函数与其最不凹的主要内容之间差异构建的统计量。这里表明，统一分布对这种测试最不利，因为在统一性下获得的统计量的限制分布随机地在任何其他凹形分布函数下占据了限制分布。
A test of the concavity of a distribution function with support contained in the unit interval may be based on a statistic constructed from the $L^p$-norm of the difference between an empirical distribution function and its least concave majorant. It is shown here that the uniform distribution is least favorable for such a test, in the sense that the limiting distribution of the statistic obtained under uniformity stochastically dominates the limiting distribution obtained under any other concave distribution function.
