Xiufang Liu, Dehui Wang, Huaping Chen, Lifang Zhao, Liang Liu
{"title":"一类用于分析癫痫发作数据和 COVID-19 数据的 kth 阶依赖性驱动随机系数混合稀疏整数值自回归过程","authors":"Xiufang Liu, Dehui Wang, Huaping Chen, Lifang Zhao, Liang Liu","doi":"10.1111/anzs.12411","DOIUrl":null,"url":null,"abstract":"<div>\n \n <p>Data related to the counting of elements of variable character are frequently encountered in time series studies. This paper brings forward a new class of <span></span><math>\n <semantics>\n <mrow>\n <mi>k</mi>\n </mrow>\n <annotation>$$ k $$</annotation>\n </semantics></math>th-order dependence-driven random coefficient mixed thinning integer-valued autoregressive time series model (DDRCMTINAR(<span></span><math>\n <semantics>\n <mrow>\n <mi>k</mi>\n </mrow>\n <annotation>$$ k $$</annotation>\n </semantics></math>)) to deal with such data. Stationarity and ergodicity properties of the proposed model are derived in detail. The unknown parameters are estimated by conditional least squares, and modified quasi-likelihood and asymptotic normality of the obtained parameter estimators is established. The performances of the adopted estimate methods are checked via simulations, which present that modified quasi-likelihood estimators perform better than the conditional least squares considering the proportion of within-<span></span><math>\n <semantics>\n <mrow>\n <mi>Ω</mi>\n </mrow>\n <annotation>$$ \\Omega $$</annotation>\n </semantics></math> estimates in certain regions of the parameter space. The validity and practical utility of the model are investigated by epileptic seizure data and COVID-19 data of suspected cases in China.</p>\n </div>","PeriodicalId":55428,"journal":{"name":"Australian & New Zealand Journal of Statistics","volume":"66 2","pages":"249-280"},"PeriodicalIF":0.8000,"publicationDate":"2024-04-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"A class of kth-order dependence-driven random coefficient mixed thinning integer-valued autoregressive process to analyse epileptic seizure data and COVID-19 data\",\"authors\":\"Xiufang Liu, Dehui Wang, Huaping Chen, Lifang Zhao, Liang Liu\",\"doi\":\"10.1111/anzs.12411\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div>\\n \\n <p>Data related to the counting of elements of variable character are frequently encountered in time series studies. This paper brings forward a new class of <span></span><math>\\n <semantics>\\n <mrow>\\n <mi>k</mi>\\n </mrow>\\n <annotation>$$ k $$</annotation>\\n </semantics></math>th-order dependence-driven random coefficient mixed thinning integer-valued autoregressive time series model (DDRCMTINAR(<span></span><math>\\n <semantics>\\n <mrow>\\n <mi>k</mi>\\n </mrow>\\n <annotation>$$ k $$</annotation>\\n </semantics></math>)) to deal with such data. Stationarity and ergodicity properties of the proposed model are derived in detail. The unknown parameters are estimated by conditional least squares, and modified quasi-likelihood and asymptotic normality of the obtained parameter estimators is established. The performances of the adopted estimate methods are checked via simulations, which present that modified quasi-likelihood estimators perform better than the conditional least squares considering the proportion of within-<span></span><math>\\n <semantics>\\n <mrow>\\n <mi>Ω</mi>\\n </mrow>\\n <annotation>$$ \\\\Omega $$</annotation>\\n </semantics></math> estimates in certain regions of the parameter space. The validity and practical utility of the model are investigated by epileptic seizure data and COVID-19 data of suspected cases in China.</p>\\n </div>\",\"PeriodicalId\":55428,\"journal\":{\"name\":\"Australian & New Zealand Journal of Statistics\",\"volume\":\"66 2\",\"pages\":\"249-280\"},\"PeriodicalIF\":0.8000,\"publicationDate\":\"2024-04-08\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Australian & New Zealand Journal of Statistics\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://onlinelibrary.wiley.com/doi/10.1111/anzs.12411\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"STATISTICS & PROBABILITY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Australian & New Zealand Journal of Statistics","FirstCategoryId":"100","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1111/anzs.12411","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"STATISTICS & PROBABILITY","Score":null,"Total":0}
A class of kth-order dependence-driven random coefficient mixed thinning integer-valued autoregressive process to analyse epileptic seizure data and COVID-19 data
Data related to the counting of elements of variable character are frequently encountered in time series studies. This paper brings forward a new class of th-order dependence-driven random coefficient mixed thinning integer-valued autoregressive time series model (DDRCMTINAR()) to deal with such data. Stationarity and ergodicity properties of the proposed model are derived in detail. The unknown parameters are estimated by conditional least squares, and modified quasi-likelihood and asymptotic normality of the obtained parameter estimators is established. The performances of the adopted estimate methods are checked via simulations, which present that modified quasi-likelihood estimators perform better than the conditional least squares considering the proportion of within- estimates in certain regions of the parameter space. The validity and practical utility of the model are investigated by epileptic seizure data and COVID-19 data of suspected cases in China.
期刊介绍：
The Australian & New Zealand Journal of Statistics is an international journal managed jointly by the Statistical Society of Australia and the New Zealand Statistical Association. Its purpose is to report significant and novel contributions in statistics, ranging across articles on statistical theory, methodology, applications and computing. The journal has a particular focus on statistical techniques that can be readily applied to real-world problems, and on application papers with an Australasian emphasis. Outstanding articles submitted to the journal may be selected as Discussion Papers, to be read at a meeting of either the Statistical Society of Australia or the New Zealand Statistical Association.
The main body of the journal is divided into three sections.
The Theory and Methods Section publishes papers containing original contributions to the theory and methodology of statistics, econometrics and probability, and seeks papers motivated by a real problem and which demonstrate the proposed theory or methodology in that situation. There is a strong preference for papers motivated by, and illustrated with, real data.
The Applications Section publishes papers demonstrating applications of statistical techniques to problems faced by users of statistics in the sciences, government and industry. A particular focus is the application of newly developed statistical methodology to real data and the demonstration of better use of established statistical methodology in an area of application. It seeks to aid teachers of statistics by placing statistical methods in context.
The Statistical Computing Section publishes papers containing new algorithms, code snippets, or software descriptions (for open source software only) which enhance the field through the application of computing. Preference is given to papers featuring publically available code and/or data, and to those motivated by statistical methods for practical problems.
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