一个基于追踪的精确预测算法,用于多变量双样本非参数测试,适用于回顾性和组序列研究
Li Zou1, Gregory Gurevich2, Ablert Vexler3
1Department of Statistics and Biostatistics, California State University, Hayward, CA, USA.
Journal of applied statistics
|August 19, 2024
概括
这项研究引入了一种新的非参数方法来比较多变量分布,确保准确的I型错误率,即使在小样本. 这种新技术为多变量两个样本问题提供了强大而精确的有限样本测试.
科学领域:
- 统计 统计 统计 统计
- 多变量分析多变量分析
- 非参数的方法 非参数的方法
背景情况:
- 对I型错误 (TIE) 率的精确控制对于多变量分布平等的非参数测试至关重要,特别是在小样本大小的情况下.
- 单变量方法的现有扩展 (例如,Kolmogorov-Smirnov,Cramér-von Mises) 在多变量设置中往往缺乏精确的零分布,这限制了它们的适用性.
- 在各种研究领域仍然需要精确的,无分布的测试来比较多变量分布.
研究的目的:
- 扩展基于密度的经验概率技术,用于多变量两样 (MTS) 问题中最强大的测试的非参数近似.
- 为控制I型错误率的MTS问题开发一个精确的有限样本测试统计.
- 提出一种适用于组顺序分析的新型MTS非参数程序.
主要方法:
- 利用多变量分布的平等性和单变量线性投影分布的平等性之间的一对一映射.
- 开发了一种通用算法,通过使用有限数量的向量组件的线性组合来简化投影的追求.
- 在回顾和组序列方式中应用了无分布策略,引入了一个新的组序列MTS非参数程序.
主要成果:
- 精确的有限样本多变量两样本测试统计数据是通过扩展的经验概率方法得出的.
- 拟议的团队顺序MTS非参数程序显示了非对称的一致性.
- 蒙特卡洛模拟证实,开发的程序在各种环境中具有高稳定的功率.
结论:
- 扩展的经验概率技术为多变量两个样本问题提供了有效的非参数解决方案,具有精确的有限样本属性.
- 新型组序列程序为在多变量设置中进行持续数据分析提供了强大的方法.
- 提出的方法显著提高了复杂数据场景中非参数统计测试的能力.
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