标题： 基于秩的平滑启发式拟合优度检验 显示英文标题

标题： Smoothing-inspired lack-of-fit tests based on ranks

摘要： 基于秩的检验被提出并进行了分析，该检验的原假设是某个回归变量对响应变量没有影响。 该检验的结构与顺序选择检验相同，但原始数据被替换为秩。 该检验是非参数的，因为它几乎可以一致地对抗任何平滑的替代方案，并且对于所有样本大小都是完全分布自由的。 获得了基于秩的顺序选择统计量的渐近分布，并发现其与原始数据对应的统计量的分布相同。 还提供了检验统计量的精确小样本临界值。 证明了所提出的秩检验的Pitman-Noether效率与顺序选择检验的效率相比非常有利。 事实上，它们的渐近相对效率与Wilcoxon符号秩检验和$t$检验的渐近相对效率相同。 一个涉及微阵列数据的例子说明了秩检验在实践中的有用性。 显示英文摘要

摘要： A rank-based test of the null hypothesis that a regressor has no effect on a response variable is proposed and analyzed. This test is identical in structure to the order selection test but with the raw data replaced by ranks. The test is nonparametric in that it is consistent against virtually any smooth alternative, and is completely distribution free for all sample sizes. The asymptotic distribution of the rank-based order selection statistic is obtained and seen to be the same as that of its raw data counterpart. Exact small sample critical values of the test statistic are provided as well. It is shown that the Pitman-Noether efficiency of the proposed rank test compares very favorably with that of the order selection test. In fact, their asymptotic relative efficiency is identical to that of the Wilcoxon signed rank and $t$-tests. An example involving microarray data illustrates the usefulness of the rank test in practice.