组合设计的均匀性和投影均匀性

IF 1.2 4区数学 Q2 STATISTICS & PROBABILITY

Statistics Pub Date : 2023-04-25 DOI:10.1080/02331888.2023.2206661

Kan Wang, Hong Qin, Zujun Ou

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引用次数: 0

摘要

本文的目的是研究用混合差异衡量的均匀性准则来评价q水平阶乘的最优折叠方案的问题。对组合设计分别定义了基于水平置换法的平均混合差和平均投影混合差，并从整体均匀性和各维度均匀性两方面探讨了最优折叠方案。分别得到了一般折叠方案下平均混合差和均匀度的紧下界，可作为搜索最优折叠方案的基准。给出了一些实例来说明理论结果。

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Uniformity and projection uniformity of combined designs

The purpose of this paper is to study the issue of employing the uniformity criterion measured by the mixture discrepancy to assess the optimal foldover plans for q-level factorials. The average mixture discrepancy and the average projection mixture discrepancy based on the level permutation method are respectively defined for combined designs, and the optimal foldover plan in terms of the overall uniformity and the uniformity of each dimension are also explored. The tight lower bounds of the average mixture discrepancy and the uniformity pattern under the general foldover plan are obtained respectively, which can be used as a benchmark for searching optimal foldover plans. Some illustrative examples are provided to show the theoretical results.

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来源期刊

Statistics 数学-统计学与概率论

CiteScore

1.00

自引率

0.00%

发文量

审稿时长

12 months

期刊介绍： Statistics publishes papers developing and analysing new methods for any active field of statistics, motivated by real-life problems. Papers submitted for consideration should provide interesting and novel contributions to statistical theory and its applications with rigorous mathematical results and proofs. Moreover, numerical simulations and application to real data sets can improve the quality of papers, and should be included where appropriate. Statistics does not publish papers which represent mere application of existing procedures to case studies, and papers are required to contain methodological or theoretical innovation. Topics of interest include, for example, nonparametric statistics, time series, analysis of topological or functional data. Furthermore the journal also welcomes submissions in the field of theoretical econometrics and its links to mathematical statistics.