{"title":"随机正交阵列抽样设计的非均匀浓度不等式","authors":"K. Laipaporn, K. Neammanee","doi":"10.5539/JMR.V1N2P78","DOIUrl":null,"url":null,"abstract":"Let $ f : [0 ; 1]^3 \\rightarrow R$ be a measurable function. In many computer experiments, we estimate the value of $\\int _{[0,1]^3} f (x) dx$ , which is the mean $ \\mu = E ( f \\circ X ), where X is a uniform random vector on the unit hypercube $[0 ; 1]^3$ . In 1992 and 1993, Owen and Tang introduced randomized orthogonal arrays to choose the sampling points to estimate the integral. In this paper, we give a non-uniform concentration inequality for randomized orthogonal array sampling designs.","PeriodicalId":45664,"journal":{"name":"Thai Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.3000,"publicationDate":"2009-08-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.5539/JMR.V1N2P78","citationCount":"4","resultStr":"{\"title\":\"A Non-uniform Concentration Inequality for Randomized Orthogonal Array Sampling Designs\",\"authors\":\"K. Laipaporn, K. Neammanee\",\"doi\":\"10.5539/JMR.V1N2P78\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Let $ f : [0 ; 1]^3 \\\\rightarrow R$ be a measurable function. In many computer experiments, we estimate the value of $\\\\int _{[0,1]^3} f (x) dx$ , which is the mean $ \\\\mu = E ( f \\\\circ X ), where X is a uniform random vector on the unit hypercube $[0 ; 1]^3$ . In 1992 and 1993, Owen and Tang introduced randomized orthogonal arrays to choose the sampling points to estimate the integral. In this paper, we give a non-uniform concentration inequality for randomized orthogonal array sampling designs.\",\"PeriodicalId\":45664,\"journal\":{\"name\":\"Thai Journal of Mathematics\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.3000,\"publicationDate\":\"2009-08-20\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.5539/JMR.V1N2P78\",\"citationCount\":\"4\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Thai Journal of Mathematics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.5539/JMR.V1N2P78\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Thai Journal of Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.5539/JMR.V1N2P78","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 4
摘要
Let $ f: [0;1]^3 \右列R$是一个可测函数。在许多计算机实验中，我们估计$\int _{[0,1]^3} f (x) dx$的值，这是平均值$\ mu = E (f \circ x)，其中x是单位超立方体$[0]上的均匀随机向量;1) ^ 3美元。1992年和1993年，Owen和Tang引入随机正交阵列来选择采样点来估计积分。本文给出了随机正交阵列抽样设计的非均匀浓度不等式。
A Non-uniform Concentration Inequality for Randomized Orthogonal Array Sampling Designs
Let $ f : [0 ; 1]^3 \rightarrow R$ be a measurable function. In many computer experiments, we estimate the value of $\int _{[0,1]^3} f (x) dx$ , which is the mean $ \mu = E ( f \circ X ), where X is a uniform random vector on the unit hypercube $[0 ; 1]^3$ . In 1992 and 1993, Owen and Tang introduced randomized orthogonal arrays to choose the sampling points to estimate the integral. In this paper, we give a non-uniform concentration inequality for randomized orthogonal array sampling designs.
期刊介绍：
Thai Journal of Mathematics (TJM) is a peer-reviewed, open access international journal publishing original research works of high standard in all areas of pure and applied mathematics.
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