{"title":"A new First-Order mixture integer-valued threshold autoregressive process based on binomial thinning and negative binomial thinning","authors":"Danshu Sheng , Dehui Wang , Liuquan Sun","doi":"10.1016/j.jspi.2023.106143","DOIUrl":null,"url":null,"abstract":"<div><p><span><span>In this paper, we introduce a new first-order mixture integer-valued threshold autoregressive process, based on the binomial and </span>negative binomial thinning operators. Basic probabilistic and statistical properties of this model are discussed. Conditional least squares (CLS) and conditional maximum likelihood (CML) estimators are derived and the </span>asymptotic properties<span> of the estimators are established. The inference for the threshold parameter is obtained based on the CLS and CML score functions<span>. Moreover, the Wald test is applied to detect the existence of the piecewise structure. Simulation studies are considered, along with an application: the number of criminal mischief incidents in the Pittsburgh dataset</span></span></p></div>","PeriodicalId":50039,"journal":{"name":"Journal of Statistical Planning and Inference","volume":"231 ","pages":"Article 106143"},"PeriodicalIF":0.8000,"publicationDate":"2023-12-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Statistical Planning and Inference","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S037837582300112X","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"STATISTICS & PROBABILITY","Score":null,"Total":0}
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Abstract
In this paper, we introduce a new first-order mixture integer-valued threshold autoregressive process, based on the binomial and negative binomial thinning operators. Basic probabilistic and statistical properties of this model are discussed. Conditional least squares (CLS) and conditional maximum likelihood (CML) estimators are derived and the asymptotic properties of the estimators are established. The inference for the threshold parameter is obtained based on the CLS and CML score functions. Moreover, the Wald test is applied to detect the existence of the piecewise structure. Simulation studies are considered, along with an application: the number of criminal mischief incidents in the Pittsburgh dataset
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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.
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