基于经验似然法的整数值 AR(1) 模型统一检验

IF 0.8 4区数学 Q3 STATISTICS & PROBABILITY

Journal of Statistical Planning and Inference Pub Date : 2024-01-26 DOI:10.1016/j.jspi.2024.106149

Jing Zhang , Bo Li , Yu Wang , Xinyi Wei , Xiaohui Liu

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引用次数: 0

摘要

本文提出了一种基于经验似然法的整数值 AR(1) 模型（即 INAR(1)）自回归系数检验方法。我们推导了所得到的检验统计量在零假设和备择假设下的极限分布。结果表明，无论 INAR 过程是稳定的还是不稳定的，该统计量在零假设下总是渐近呈奇平方分布，因此可以为自回归系数提供统一的推断。此外，还通过模拟和一个经验实例证明了其有限样本的性能。

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An empirical likelihood-based unified test for the integer-valued AR(1) models

In this paper, we suggest an empirical likelihood-based test for the autoregressive coefficient of an integer-valued AR(1) model, i.e., INAR(1). We derive the limit distributions of the resulting test statistic under both null and alternative hypotheses. It turns out that regardless of whether the INAR process is stable or unstable, the statistic is always chi-squared distributed asymptotically under the null hypothesis, and as a result, it can offer unified inferences for the autoregressive coefficient. The performance of its finite sample is also demonstrated using simulations and an empirical example.

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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.