MAXIMALLY SELECTED RANK STATISTICS
MAXIMALLY SELECTED RANK STATISTICS
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DOI：
10.2307/2532740
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发表时间：
1992-03-01
期刊：
影响因子：
1.9
通讯作者：
SCHUMACHER, M
中科院分区：
文献类型：
--
作者：
LAUSEN, B;SCHUMACHER, M
一个常见的统计问题是评估定量变量对因变量的预测能力。关于定量变量的最大选择秩统计量提供了一个检验，并隐含地作为一个简单的分类规则的临界点的估计。限制选择到一个任意给定的内部部分的支持的定量变量，我们表明，最大选择的秩统计量的渐近零分布是一个标准化的高斯过程的绝对值的上确界的分布在一个区间。渐近参数也适用于捆绑或截尾观测的情况。我们比较Monte Carlo结果与零假设下的渐近分布的近似。此外，我们调查的行为的测试程序和熟悉的斯皮尔曼秩检验的独立性，在一些替代品。此外，我们讨论了一些方面的问题，估计一个潜在的切割点。
A common statistical problem is the assessment of the predictive power of a quantitative variable for some dependent variable. A maximally selected rank statistic regarding the quantitative variable provides a test and implicitly an estimate of a cutpoint as a simple classification rule. Restricting the selection to an arbitrary given inner part of the support of the quantitative variable, we show that the asymptotic null distribution of the maximally selected rank statistic is the distribution of the supremum of the absolute value of a standardized Gaussian process on an interval. The asymptotic argument holds also in the case of tied or censored observations.We compare Monte Carlo results with an approximation of the asymptotic distribution under the null hypothesis. In addition, we investigate the behaviour of the test procedure and of the familiar Spearman rank test for independence, under some alternatives. Moreover, we discuss some aspects of the problem of estimating an underlying cutpoint.