{"title":"A class of mixed-level uniform designs generated by code mapping","authors":"Liuping Hu , Zujun Ou , Hong Qin","doi":"10.1016/j.jspi.2024.106166","DOIUrl":null,"url":null,"abstract":"<div><p>Literature reviews reveal that there is a very close connection between experimental design and coding theory. Based on a code mapping transformation, this paper provides a new method to construct a class of mixed designs with two- and four-level. A general construction method is described and some theoretical results of obtained designs are given. Analytic connections are established between the generated and the initial designs in terms of aberration criteria and discrepancies. Sharp lower bounds of the wrap-around <span><math><msub><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span>- and Lee discrepancies are obtained and used as the benchmarks to measure the uniformity of the generated designs. Examples are provided to illustrate the effectiveness of the construction and lend our results further support.</p></div>","PeriodicalId":50039,"journal":{"name":"Journal of Statistical Planning and Inference","volume":"233 ","pages":"Article 106166"},"PeriodicalIF":0.8000,"publicationDate":"2024-03-24","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/S0378375824000235","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
Abstract
Literature reviews reveal that there is a very close connection between experimental design and coding theory. Based on a code mapping transformation, this paper provides a new method to construct a class of mixed designs with two- and four-level. A general construction method is described and some theoretical results of obtained designs are given. Analytic connections are established between the generated and the initial designs in terms of aberration criteria and discrepancies. Sharp lower bounds of the wrap-around - and Lee discrepancies are obtained and used as the benchmarks to measure the uniformity of the generated designs. Examples are provided to illustrate the effectiveness of the construction and lend our results further support.
文献综述显示，实验设计与编码理论之间有着非常密切的联系。本文以编码映射变换为基础，提供了一种构建两水平和四水平混合设计的新方法。本文描述了一般构建方法，并给出了所获设计的一些理论结果。从像差标准和差异的角度，在生成的设计和初始设计之间建立了分析联系。获得了环绕 L2- 和 Lee 差异的尖锐下限，并将其作为衡量生成设计均匀性的基准。我们还举例说明了这种构造的有效性，并为我们的结果提供了进一步的支持。
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.
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