A robust partial least squares approach for function-on-function regression

IF 0.6 4区 数学 Q4 STATISTICS & PROBABILITY
U. Beyaztas, H. Shang
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引用次数: 0

Abstract

The function-on-function linear regression model in which the response and predictors consist of random curves has become a general framework to investigate the relationship between the functional response and functional predictors. Existing methods to estimate the model parameters may be sensitive to outlying observations, common in empirical applications. In addition, these methods may be severely affected by such observations, leading to undesirable estimation and prediction results. A robust estimation method, based on iteratively reweighted simple partial least squares, is introduced to improve the prediction accuracy of the function-on-function linear regression model in the presence of outliers. The performance of the proposed method is based on the number of partial least squares components used to estimate the function-on-function linear regression model. Thus, the optimum number of components is determined via a data-driven error criterion. The finite-sample performance of the proposed method is investigated via several Monte Carlo experiments and an empirical data analysis. In addition, a nonparametric bootstrap method is applied to construct pointwise prediction intervals for the response function. The results are compared with some of the existing methods to illustrate the improvement potentially gained by the proposed method.
函数上函数回归的一种稳健偏最小二乘方法
反应和预测因子由随机曲线组成的函数对函数线性回归模型已成为研究功能反应和功能预测因子之间关系的通用框架。现有的估计模型参数的方法可能对外围观测结果敏感,这在经验应用中很常见。此外,这些方法可能会受到此类观测的严重影响,导致不期望的估计和预测结果。在存在异常值的情况下,引入了一种基于迭代重加权简单偏最小二乘的稳健估计方法,以提高函数对函数线性回归模型的预测精度。所提出的方法的性能是基于用于估计函数上函数线性回归模型的偏最小二乘分量的数量。因此,通过数据驱动的误差准则来确定部件的最佳数量。通过几个蒙特卡罗实验和经验数据分析,研究了该方法的有限样本性能。此外,还应用了一种非参数自举方法来构造响应函数的逐点预测区间。将结果与现有的一些方法进行了比较,以说明所提出的方法可能获得的改进。
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来源期刊
CiteScore
1.60
自引率
10.00%
发文量
30
审稿时长
>12 weeks
期刊介绍: The Brazilian Journal of Probability and Statistics aims to publish high quality research papers in applied probability, applied statistics, computational statistics, mathematical statistics, probability theory and stochastic processes. More specifically, the following types of contributions will be considered: (i) Original articles dealing with methodological developments, comparison of competing techniques or their computational aspects. (ii) Original articles developing theoretical results. (iii) Articles that contain novel applications of existing methodologies to practical problems. For these papers the focus is in the importance and originality of the applied problem, as well as, applications of the best available methodologies to solve it. (iv) Survey articles containing a thorough coverage of topics of broad interest to probability and statistics. The journal will occasionally publish book reviews, invited papers and essays on the teaching of statistics.
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