Comparing regression curves: an L1-point of view

IF 0.8 4区数学 Q3 STATISTICS & PROBABILITY

Annals of the Institute of Statistical Mathematics Pub Date : 2023-08-30 DOI:10.1007/s10463-023-00880-8

Patrick Bastian, Holger Dette, Lukas Koletzko, Kathrin Möllenhoff

引用次数: 0

Abstract

In this paper, we compare two regression curves by measuring their difference by the area between the two curves, represented by their \(L^1\)-distance. We develop asymptotic confidence intervals for this measure and statistical tests to investigate the similarity/equivalence of the two curves. Bootstrap methodology specifically designed for equivalence testing is developed to obtain procedures with good finite sample properties and its consistency is rigorously proved. The finite sample properties are investigated by means of a small simulation study.

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比较回归曲线：从 L1 角度看问题

在本文中，我们通过两条曲线之间的面积（用它们的 \(L^1\)-distance 表示）来测量它们的差异，从而比较两条回归曲线。我们为这一度量建立了渐近置信区间，并通过统计检验来研究两条曲线的相似性/等价性。我们开发了专门用于等价性检验的 Bootstrap 方法，以获得具有良好有限样本特性的程序，并严格证明了其一致性。通过一项小型模拟研究对有限样本特性进行了调查。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Annals of the Institute of Statistical Mathematics 数学-统计学与概率论

CiteScore

2.00

自引率

0.00%

发文量

审稿时长

6-12 weeks

期刊介绍： Annals of the Institute of Statistical Mathematics (AISM) aims to provide a forum for open communication among statisticians, and to contribute to the advancement of statistics as a science to enable humans to handle information in order to cope with uncertainties. It publishes high-quality papers that shed new light on the theoretical, computational and/or methodological aspects of statistical science. Emphasis is placed on (a) development of new methodologies motivated by real data, (b) development of unifying theories, and (c) analysis and improvement of existing methodologies and theories.