Inference for trend functions in partially linear models

IF 0.8 4区数学 Q3 STATISTICS & PROBABILITY

Journal of Statistical Planning and Inference Pub Date : 2025-09-02 DOI:10.1016/j.jspi.2025.106338

Sijie Zheng , Xiaojun Song

引用次数: 0

Abstract

A nonparametric test is developed to determine whether the trend of a partially linear model (PLM) with dependent errors and locally stationary regressors follows a specific parametric form. The test is asymptotically normal under the null hypothesis of correct trend specification and is consistent against various alternatives that deviate from the null hypothesis. The testing power against two classes of local alternatives approaching the null at different rates is derived, along with the asymptotic distribution of the test under fixed alternatives. We also propose a wild bootstrap procedure to better approximate the finite sample null distribution of the test. Statistical inference is performed on the trend specification in the Phillips curve and ozone concentration.

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部分线性模型中趋势函数的推断

提出了一种非参数检验方法，以确定具有相关误差和局部平稳回归量的部分线性模型（PLM）的趋势是否遵循特定参数形式。在正确趋势规范的零假设下，检验是渐近正态的，并且对于偏离零假设的各种替代方案是一致的。导出了针对两类以不同速率接近零的局部选择的检验能力，以及在固定选择下检验的渐近分布。我们还提出了一个野生自举过程，以更好地近似检验的有限样本零分布。对菲利普斯曲线的趋势规范和臭氧浓度进行了统计推断。

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

Journal of Statistical Planning and Inference 数学-统计学与概率论

CiteScore

2.10

自引率

11.10%

发文量

审稿时长

3-6 weeks

期刊介绍： The Journal of Statistical Planning and Inference offers itself as a multifaceted and all-inclusive bridge between classical aspects of statistics and probability, and the emerging interdisciplinary aspects that have a potential of revolutionizing the subject. While we maintain our traditional strength in statistical inference, design, classical probability, and large sample methods, we also have a far more inclusive and broadened scope to keep up with the new problems that confront us as statisticians, mathematicians, and scientists. We publish high quality articles in all branches of statistics, probability, discrete mathematics, machine learning, and bioinformatics. We also especially welcome well written and up to date review articles on fundamental themes of statistics, probability, machine learning, and general biostatistics. Thoughtful letters to the editors, interesting problems in need of a solution, and short notes carrying an element of elegance or beauty are equally welcome.