推荐(稳健)非线性回归方法的统计学习

IF 0.3 Q4 MATHEMATICS, APPLIED
J. Kalina, J. Tichavský
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引用次数: 1

摘要

摘要我们感兴趣的是比较标准非线性回归模型参数的各种非线性估计量的性能。虽然标准非线性最小二乘估计器容易受到数据中存在异常测量的影响,但存在几种稳健的替代方案。然而,对于给定的数据集,应该使用哪个估计器还不清楚,这个问题在理论上仍然非常难以回答(或者可能不可行)。元学习代表了一种用于优化算法(或方法)的计算密集型方法,并且在这里用于预测特定数据集的最合适的非线性估计器。分类规则是在24个公开可用数据集的训练数据库上学习的。初级学习的结果为非线性最小二乘估计提供了一个有趣的论据,它被证明是最适合大多数数据集的估计。随后的元学习表明,正态性和异方差检验在寻找最合适的非线性估计器方面起着至关重要的作用。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Statistical learning for recommending (robust) nonlinear regression methods
Abstract We are interested in comparing the performance of various nonlinear estimators of parameters of the standard nonlinear regression model. While the standard nonlinear least squares estimator is vulnerable to the presence of outlying measurements in the data, there exist several robust alternatives. However, it is not clear which estimator should be used for a given dataset and this question remains extremely difficult (or perhaps infeasible) to be answered theoretically. Metalearning represents a computationally intensive methodology for optimal selection of algorithms (or methods) and is used here to predict the most suitable nonlinear estimator for a particular dataset. The classification rule is learned over a training database of 24 publicly available datasets. The results of the primary learning give an interesting argument in favor of the nonlinear least weighted squares estimator, which turns out to be the most suitable one for the majority of datasets. The subsequent metalearning reveals that tests of normality and heteroscedasticity play a crucial role in finding the most suitable nonlinear estimator.
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