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A goodness‐of‐fit test for the functional linear model with functional response
Scandinavian Journal of Statistics ( IF 1 ) Pub Date : 2020-09-14 , DOI: 10.1111/sjos.12486
Eduardo García‐Portugués 1, 2 , Javier Álvarez‐Liébana 3 , Gonzalo Álvarez‐Pérez 4 , Wenceslao González‐Manteiga 5
Affiliation  

The Functional Linear Model with Functional Response (FLMFR) is one of the most fundamental models to asses the relation between two functional random variables. In this paper, we propose a novel goodness-of-fit test for the FLMFR against a general, unspecified, alternative. The test statistic is formulated in terms of a Cramer-von Mises norm over a doubly-projected empirical process which, using geometrical arguments, yields an easy-to-compute weighted quadratic norm. A resampling procedure calibrates the test through a wild bootstrap on the residuals and the use convenient computational procedures. As a sideways contribution, and since the statistic requires from a reliable estimator of the FLMFR, we discuss and compare several regularized estimators, providing a new one specifically convenient for our test. The finite sample behavior of the test, regarding power and size, is illustrated via a complete simulation study. Also, the new proposal is compared with previous significance tests. Two novel real datasets illustrate the application of the new test.

中文翻译:

具有函数响应的函数线性模型的拟合优度检验

具有函数响应的函数线性模型 (FLMFR) 是评估两个函数随机变量之间关系的最基本模型之一。在本文中,我们针对通用的、未指定的替代方案提出了一种新的 FLMFR 拟合优度检验。检验统计量是根据双投影经验过程中的 Cramer-von Mises 范数制定的,该过程使用几何参数产生易于计算的加权二次范数。重采样程序通过残差上的野生引导程序和使用方便的计算程序来校准测试。作为横向贡献,并且由于统计需要来自 FLMFR 的可靠估计器,我们讨论并比较了几个正则化估计器,为我们的测试提供了一个特别方便的新估计器。测试的有限样本行为,关于功率和大小,通过完整的模拟研究来说明。此外,新提案与之前的显着性检验进行了比较。两个新颖的真实数据集说明了新测试的应用。
更新日期:2020-09-14
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