在回归模型中定位平滑项差异的同时置信度受限的真实发现比例视角
1University of Texas MD Anderson Cancer Center, Houston, TX, USA.
Computational statistics & data analysis
|June 20, 2025
概括
本研究引入了一种新的方法,用于使用真实发现比例 (TDP) 估计来识别两个光滑之间的差异. 该方法提供了对特定地区真实差异比例的信心局限性陈述,提高了统计的严谨性.
科学领域:
- 统计建模 统计建模
- 非参数的回归分析分析.
- 数据解释 数据解释
背景情况:
- 在统计分析中,精确地定位平滑函数之间的差异至关重要.
- 现有的方法通常依赖于特设方法,例如数据子集和假设测试,这些方法可能缺乏严格性.
- 需要统计学上合理的方法来量化平滑项之间的分歧区域.
研究的目的:
- 开发和演示一种方法来定位两个spline项 (smooths) 之间的差异.
- 提供关于特定区域内真实差异的比例的可信度限制的陈述.
- 提供一个统计严格的替代方法,以比较平滑的ad hoc方法.
主要方法:
- 使用基于真实发现比例 (TDP) 的解释来进行本地化.
- 采用基于西姆斯局部测试的封闭测试程序.
- 依赖于广义的Wishart类型的多变量chi平方测试统计数据,假设对子集的正回归依赖性 (PRDS).
主要成果:
- 该方法产生了关于区域比例的陈述,在这些地区之间存在真正的差异.
- 与此同时,TDP估计是有信心限制的 (1-α),为高信心的真实发现提供了下限.
- 对于由REML或GCV选择的调参数的通用添加模型,证明了一致性.
结论:
- 拟议的方法提供了一个统计学上可靠的方法来识别和量化光滑之间的差异.
- 有信心的TDP提供了真实发现的可靠估计,不管进行了多少次比较.
- 该方法通过模拟研究得到验证,并应用于分析行走步态数据.
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