Comparing time varying regression quantiles under shift invariance

IF 1.5 2区数学 Q2 STATISTICS & PROBABILITY

Bernoulli Pub Date : 2023-05-01 DOI:10.3150/22-bej1509

S. S. Dhar, Weichi Wu

引用次数: 2

Abstract

This article investigates whether time-varying quantile regression curves are the same up to the horizontal shift or not. The errors and the covariates involved in the regression model are allowed to be locally stationary. We formalize this issue in a corresponding non-parametric hypothesis testing problem, and develop an integrated-squared-norm based test (SIT) as well as a simultaneous confidence band (SCB) approach. The asymptotic properties of SIT and SCB under null and local alternatives are derived. Moreover, the asymptotic properties of these tests are also studied when the compared data sets are dependent. We then propose valid wild bootstrap algorithms to implement SIT and SCB. Furthermore, the usefulness of the proposed methodology is illustrated via analysing simulated and real data related to COVID-19 outbreak and climate science. bootstrap, comparison of curves, confidence band, hypothesis testing, locally stationary process, nonparametric quantile regression, COVID-19. 1 ar X iv :2 01 1. 06 33 3v 2 [ st at .M E ] 2 4 D ec 2 02 1

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移位不变性下时变回归分位数的比较

本文研究了时变分位数回归曲线在水平位移之前是否相同。回归模型中涉及的误差和协变量被允许是局部平稳的。我们将这个问题形式化为相应的非参数假设检验问题，并开发了一种基于平方范数的综合检验（SIT）和同时置信带（SCB）方法。导出了SIT和SCB在零和局部替换下的渐近性质。此外，当比较的数据集是相依的时，还研究了这些检验的渐近性质。然后，我们提出了有效的野生自举算法来实现SIT和SCB。此外，通过分析与新冠肺炎疫情和气候科学相关的模拟和真实数据，说明了拟议方法的有用性。bootstrap、曲线比较、置信区间、假设检验、局部平稳过程、非参数分位数回归、新冠肺炎。1 ar X iv：2 01 1。06 33 3v 2[st at.M E]2 4 D ec 2 02 1

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来源期刊

Bernoulli 数学-统计学与概率论

CiteScore

3.40

自引率

0.00%

发文量

116

审稿时长

6-12 weeks

期刊介绍： BERNOULLI is the journal of the Bernoulli Society for Mathematical Statistics and Probability, issued four times per year. The journal provides a comprehensive account of important developments in the fields of statistics and probability, offering an international forum for both theoretical and applied work. BERNOULLI will publish: Papers containing original and significant research contributions: with background, mathematical derivation and discussion of the results in suitable detail and, where appropriate, with discussion of interesting applications in relation to the methodology proposed. Papers of the following two types will also be considered for publication, provided they are judged to enhance the dissemination of research: Review papers which provide an integrated critical survey of some area of probability and statistics and discuss important recent developments. Scholarly written papers on some historical significant aspect of statistics and probability.