Fuzzy versus statistical linear regression
Fuzzy versus statistical linear regression
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DOI：
10.1016/0377-2217(94)00352-1
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发表时间：
1996-07-19
影响因子：
6.4
通讯作者：
Koksalan, M
中科院分区：
文献类型：
--
作者：
Kim, KJ;Moskowitz, H;Koksalan, M
统计线性回归和模糊线性回归是从不同的角度发展起来的，因此这两种方法在概念和方法上存在一些差异。描述并对比了两种方法在基本假设、参数估计和应用方面的特点。他们的描述能力和预测能力也通过模拟实验进行了比较，以确定其中一种表现优于另一种的条件。结果表明，统计线性回归在预测能力方面优于模糊线性回归，但它们的相对描述性能取决于与数据集相关的各种因素(大小、质量)和适当的模型特定性(模型的适宜性、异方差、自相关性、误差项的非随机性)。具体地说，与统计线性回归相比，模糊线性回归的性能随着数据集的减小和回归模型的适宜性的恶化而变得相对更好。因此，当数据集不足以支持统计回归分析和/或回归模型的适宜性较差(例如，由于变量之间的模糊关系和较差的模型规范)时，模糊线性回归可以用作估计回归参数的统计线性回归的可行备选方案。
Statistical linear regression and fuzzy linear regression have been developed from different perspectives, and thus there exist several conceptual and methodological differences between the two approaches. The characteristics of both methods, in terms of basic assumptions, parameter estimation, and application are described and contrasted. Their descriptive and predictive capabilities are also compared via a simulation experiment to identify the conditions under which one outperforms the other. It turns out that statistical linear regression is superior to fuzzy linear regression in terms of predictive capability, whereas their comparative descriptive performance depends on various factors associated with the data set (size, quality) and proper specificity of the model (aptness of the model, heteroscedasticity, autocorrelation, nonrandomness of error terms). Specifically, fuzzy linear regression performance becomes relatively better, vis-a-vis statistical linear regression, as the size of the data set diminishes and the aptness of the regression model deteriorates. Fuzzy linear regression may thus be used as a viable alternative to statistical linear regression in estimating regression parameters when the data set is insufficient to support statistical regression analysis and/or the aptness of the regression model is poor (e.g., due to vague relationship among variables and poor model specification).