分叉马尔可夫链中过渡密度的核估计

IF 0.8 4区数学 Q3 STATISTICS & PROBABILITY

Journal of Statistical Planning and Inference Pub Date : 2023-12-20 DOI:10.1016/j.jspi.2023.106138

S. Valère Bitseki Penda

{"title":"分叉马尔可夫链中过渡密度的核估计","authors":"S. Valère Bitseki Penda","doi":"10.1016/j.jspi.2023.106138","DOIUrl":null,"url":null,"abstract":"<div><p><span>We study the kernel estimators<span><span> of the transition density of bifurcating Markov chains. Under some ergodic and </span>regularity properties, we prove that these estimators are consistent and asymptotically normal. Next, in the </span></span>numerical studies, we propose two data-driven methods to choose the bandwidth parameters. These methods, based on the so-called two bandwidths approach, are adaptation for bifurcating Markov chains of the least squares Cross-Validation and the rule of thumb method. Finally, we provide an example with real data.</p></div>","PeriodicalId":50039,"journal":{"name":"Journal of Statistical Planning and Inference","volume":"231 ","pages":"Article 106138"},"PeriodicalIF":0.8000,"publicationDate":"2023-12-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Kernel estimation of the transition density in bifurcating Markov chains\",\"authors\":\"S. Valère Bitseki Penda\",\"doi\":\"10.1016/j.jspi.2023.106138\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p><span>We study the kernel estimators<span><span> of the transition density of bifurcating Markov chains. Under some ergodic and </span>regularity properties, we prove that these estimators are consistent and asymptotically normal. Next, in the </span></span>numerical studies, we propose two data-driven methods to choose the bandwidth parameters. These methods, based on the so-called two bandwidths approach, are adaptation for bifurcating Markov chains of the least squares Cross-Validation and the rule of thumb method. Finally, we provide an example with real data.</p></div>\",\"PeriodicalId\":50039,\"journal\":{\"name\":\"Journal of Statistical Planning and Inference\",\"volume\":\"231 \",\"pages\":\"Article 106138\"},\"PeriodicalIF\":0.8000,\"publicationDate\":\"2023-12-20\",\"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/S0378375823001076\",\"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":"Journal of Statistical Planning and Inference","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0378375823001076","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"STATISTICS & PROBABILITY","Score":null,"Total":0}

引用次数: 0

摘要

我们研究了分叉马尔可夫链过渡密度的核估计量。在一些遍历和正则特性下，我们证明了这些估计值是一致和渐近正态的。接下来，在数值研究中，我们提出了两种数据驱动的带宽参数选择方法。这些方法基于所谓的双带宽方法，适用于最小二乘交叉验证法和经验法则法的分叉马尔可夫链。最后，我们提供了一个使用真实数据的示例。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Kernel estimation of the transition density in bifurcating Markov chains

We study the kernel estimators of the transition density of bifurcating Markov chains. Under some ergodic and regularity properties, we prove that these estimators are consistent and asymptotically normal. Next, in the numerical studies, we propose two data-driven methods to choose the bandwidth parameters. These methods, based on the so-called two bandwidths approach, are adaptation for bifurcating Markov chains of the least squares Cross-Validation and the rule of thumb method. Finally, we provide an example with real data.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

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.