{"title":"Jittering and clustering: strategies for the construction of robust designs","authors":"Douglas P. Wiens","doi":"10.1007/s11222-024-10436-2","DOIUrl":null,"url":null,"abstract":"<p>We discuss, and give examples of, methods for randomly implementing some minimax robust designs from the literature. These have the advantage, over their deterministic counterparts, of having bounded maximum loss in large and very rich neighbourhoods of the, almost certainly inexact, response model fitted by the experimenter. Their maximum loss rivals that of the theoretically best possible, but not implementable, minimax designs. The procedures are then extended to more general robust designs. For two-dimensional designs we sample from contractions of Voronoi tessellations, generated by selected basis points, which partition the design space. These ideas are then extended to <i>k</i>-dimensional designs for general <i>k</i>.</p>","PeriodicalId":22058,"journal":{"name":"Statistics and Computing","volume":"418 1","pages":""},"PeriodicalIF":1.6000,"publicationDate":"2024-06-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Statistics and Computing","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s11222-024-10436-2","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"COMPUTER SCIENCE, THEORY & METHODS","Score":null,"Total":0}
引用次数: 0
Abstract
We discuss, and give examples of, methods for randomly implementing some minimax robust designs from the literature. These have the advantage, over their deterministic counterparts, of having bounded maximum loss in large and very rich neighbourhoods of the, almost certainly inexact, response model fitted by the experimenter. Their maximum loss rivals that of the theoretically best possible, but not implementable, minimax designs. The procedures are then extended to more general robust designs. For two-dimensional designs we sample from contractions of Voronoi tessellations, generated by selected basis points, which partition the design space. These ideas are then extended to k-dimensional designs for general k.
我们将讨论并举例说明随机实施文献中某些最小稳健设计的方法。与确定性设计相比，这些设计的优点是在实验者拟合的反应模型（几乎可以肯定是不精确的）的大而丰富的邻域内具有有界最大损失。它们的最大损失可与理论上最佳但无法实施的最小设计相媲美。然后，我们将程序扩展到更一般的稳健设计。对于二维设计，我们从由选定基点生成的 Voronoi 网格收缩中进行采样，从而分割设计空间。然后，我们将这些想法扩展到一般 k 的 k 维设计。
期刊介绍：
Statistics and Computing is a bi-monthly refereed journal which publishes papers covering the range of the interface between the statistical and computing sciences.
In particular, it addresses the use of statistical concepts in computing science, for example in machine learning, computer vision and data analytics, as well as the use of computers in data modelling, prediction and analysis. Specific topics which are covered include: techniques for evaluating analytically intractable problems such as bootstrap resampling, Markov chain Monte Carlo, sequential Monte Carlo, approximate Bayesian computation, search and optimization methods, stochastic simulation and Monte Carlo, graphics, computer environments, statistical approaches to software errors, information retrieval, machine learning, statistics of databases and database technology, huge data sets and big data analytics, computer algebra, graphical models, image processing, tomography, inverse problems and uncertainty quantification.
In addition, the journal contains original research reports, authoritative review papers, discussed papers, and occasional special issues on particular topics or carrying proceedings of relevant conferences. Statistics and Computing also publishes book review and software review sections.
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