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Prequential Analysis of Complex Data with Adaptive Model Reselection.
Statistical Analysis and Data Mining ( IF 1.3 ) Pub Date : 2009-10-14 , DOI: 10.1002/sam.10052
Jennifer Clarke 1 , Bertrand Clarke
Affiliation  

In Prequential analysis, an inference method is viewed as a forecasting system, and the quality of the inference method is based on the quality of its predictions. This is an alternative approach to more traditional statistical methods that focus on the inference of parameters of the data generating distribution. In this paper, we introduce adaptive combined average predictors (ACAPs) for the Prequential analysis of complex data. That is, we use convex combinations of two different model averages to form a predictor at each time step in a sequence. A novel feature of our strategy is that the models in each average are re‐chosen adaptively at each time step. To assess the complexity of a given data set, we introduce measures of data complexity for continuous response data. We validate our measures in several simulated contexts prior to using them in real data examples. The performance of ACAPs is compared with the performances of predictors based on stacking or likelihood weighted averaging in several model classes and in both simulated and real data sets. Our results suggest that ACAPs achieve a better trade off between model list bias and model list variability in cases where the data is very complex. This implies that the choices of model class and averaging method should be guided by a concept of complexity matching, i.e. the analysis of a complex data set may require a more complex model class and averaging strategy than the analysis of a simpler data set. We propose that complexity matching is akin to a bias‐variance tradeoff in statistical modeling. Copyright © 2009 Wiley Periodicals, Inc. Statistical Analysis and Data Mining 2: 000‐000, 2009

中文翻译:

使用自适应模型重选对复杂数据进行前置分析。

在 Prequential 分析中,推理方法被视为一个预测系统,推理方法的质量取决于其预测的质量。这是更传统的统计方法的替代方法,这些方法侧重于推断数据生成分布的参数。在本文中,我们引入了自适应组合平均预测器 (ACAP),用于复杂数据的先验分析。也就是说,我们使用两个不同模型平均值的凸组合来形成序列中每个时间步的预测器。我们策略的一个新特点是在每个时间步自适应地重新选择每个平均值中的模型。为了评估给定数据集的复杂性,我们引入了连续响应数据的数据复杂性度量。在实际数据示例中使用之前,我们在几个模拟环境中验证了我们的措施。将 ACAP 的性能与基于堆叠或似然加权平均的预测器在多个模型类以及模拟和真实数据集中的性能进行比较。我们的结果表明,在数据非常复杂的情况下,ACAP 在模型列表偏差和模型列表可变性之间实现了更好的权衡。这意味着模型类和平均方法的选择应该以复杂性匹配的概念为指导,即复杂数据集的分析可能比简单数据集的分析需要更复杂的模型类和平均策略。我们建议复杂性匹配类似于统计建模中的偏差-方差权衡。版权所有 © 2009 Wiley Periodicals, Inc.
更新日期:2009-10-14
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