A new development of a conditional test (specially its sequential version) for contingency tables and the related problems

列联表条件测试（特别是其顺序版本）的新发展及相关问题

• 批准号: 13640121
• 负责人: SAKATA Toshio
• 金额: $ 1.66万
• 依托单位: Kyushu Institute of Design
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2001
• 资助国家: 日本
• 起止时间: 2001 至 2002
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-13640121/
• 关键词: Contingency tables; Conditional exact test; Creation Operator; Size of the test; Power of the sequential test; Quantum MCMC on the set of contingency tables; Three way tables; MCMC in constrained inference; 条検付正確検定; クリエーシヨン作用素; 不等式制約下の相関行列のMCMC推

The aim of this research was to develop a theory of the sequential conditional test for contingency tables. The sequential conditional test was constructed via the creation operator for A-hypergeometric partial differential equation systems. This idea was motivated by the works of Takayama et al. for integer programming problems. The implementation problem of the test and its power performance for the two way tables was examined in the year 2001. It was shown that for moderate size of two way tables the sequential test performs well on PC. The result was published in the several international conference, ICPR in Prague and 53^<rd> ISI in Seoul and ICNCB in Osaka. The second year 2002, we attacked the construction of the sequential conditional test for three way tables of type 3x3x3. The performance was good. The result was published in the international conference SCI2002, in Florida. Then our sequential test is based on the minimal Markov basis developed by Takemura and Aoki. Therefor … More e we are now pursuing the algebraic theory of constructing minimal Markov basis for three way tables initiated by Takemura and Aoki. The recent development of the algebraic theory of MCMC on the set of contingency tables was discussed in our special lecture of 16^<th> annual meeting of the Japanese computational statistical society. Further Sakata and Sawae considered the quantum version of Metropolis walk on the set of contingency tables. This was published in Journal of quantum chemistry. Further Sakata, Sawae and Nomakuchi considered the Gibbs walks on the set of correlation matrix for the constraind hypothesis of components correlation. This was published the book of Advance in Statistics, Combinatrics and related fields edited by Chandra Gulti et.al. Sakata and Jeffery Xu Yu published in Wireless Network about the estimating problem of access frequency from the request. Sasabuchi published two paper for the worldwide famous journal about the restricted inference. Nomakuchi published three papers about restricted inference. Jeferry Xu Yu published many papers and gave talks at many international conferences about Data Mining. As a result our project produced several refereed papers successfully. Less

本研究的目的是发展列联表的序贯条件检验理论。利用A-超几何偏微分方程组的生成算子构造了序贯条件检验。这个想法是由Takayama等人的作品激发的。用于整数规划问题。2001年对双向转台测试的实施问题及其功率性能进行了研究。结果表明，对于中等大小的双向表，序贯检验在PC机上进行得很好。结果发表在布拉格的ICPR、首尔的ISI和大阪的ICNCB等几个国际会议上。2002年第二年，我们抨击了3x3x3型三因素表序贯条件检验的构造。表演得很好。这一结果发表在佛罗里达州举行的国际会议SCI2002上。然后，我们的序贯检验是基于Takemura和Aoki提出的最小马尔可夫基。因此，…更重要的是，我们正在追寻由Takemura和Aoki提出的构造三向表的极小马氏基的代数理论。在日本计算统计学会第16届年会专题讲座中，讨论了列联表上MCMC代数理论的最新发展。Sakata和Sawae进一步考虑了Metropolis在列联表集合上行走的量子版本。这项研究发表在《量子化学杂志》上。在此基础上，Sakata、Sawae和Nomakuchi考虑了Gibbs游动在相关矩阵集合上的成分相关性约束假设。这本书出版了钱德拉·古尔蒂等人编辑的《统计学、组合学及相关领域的进展》一书。Sakata和Jeffery Xu Yu在《无线网络》上发表了关于从请求中估计接入频率的问题。Sasabuchi为世界著名期刊发表了两篇关于限制性推理的论文。野口发表了三篇关于限制性推理的论文。杰弗瑞·徐宇发表了多篇关于数据挖掘的论文，并在多个国际会议上发表了演讲。因此，我们的项目成功地产生了几篇参考论文。较少

项目成果

Nomakuchi, K.: "On the algorithm of Dykstra in a quadratic programming problem on a closed convex cone"Mem.Fac.Sci.Kochi Univ.(Math.). Vol 24(掲載予定). (2003)

Nomakuchi, K.：“关于闭凸锥二次规划问题中的 Dykstra 算法”Mem.Fac.Sci.Kochi Univ.（数学）第 24 卷（待出版）。

Nomakuchi,K.: "On the algorithm of Dykstra in a quadratic programming problem on a closed convex cone"Mem. Fac. Sci. Kochi. Univ. (Math.). 24(to be published). (2003)

Nomakuchi,K.：“闭凸锥二次规划问题中的 Dykstra 算法”Mem。

Sakata, T., Xy Yu J.: "Statistical Estimation of Access Frequencies : Problems, Solutions and Consistencies"Wireless Networks. (掲載予定). (2003)

Sakata, T., Xy Yu J.：“访问频率的统计估计：问题、解决方案和一致性”无线网络（即将出版）。

Sasabuchi, S., Tahaka K., Tsukamoto, T.: "Testing homogeneity of multivariate normal mean vectors under an order restriction when the covariance matrices are common but unknown"The Annals of Statistics. (掲載予定). (2003)

Sasabuchi, S.、Tahaka K.、Tsukamoto, T.：“当协方差矩阵常见但未知时，在阶数限制下测试多元正态平均向量的同质性”统计年鉴（2003 年）。

Sakata, T., Sawae, R., Nomakuchi, K.: "Maximum likelihood estimation of correlation matrix under inequality constraints using Gibbs sampling"Advances in Statistics, Combinatorics and Related Areas, World Scientific Chandra Gulati, Yan-Xia Lin, Satya Misha

Sakata, T.、Sawae, R.、Nomakuchi, K.：“使用吉布斯抽样在不平等约束下相关矩阵的最大似然估计”统计、组合学和相关领域的进展，世界科学 Chandra Gulati、Yan-Xia Lin、Satya Misha