标题： 在矩阵的行和列上存在顺序限制下的统计推断，以及在毒理学中的应用 显示英文标题

标题： Statistical inference under order restrictions on both rows and columns of a matrix, with an application in toxicology

摘要： 我们提出了一种通用的方法，用于对实值矩阵参数的组成部分进行统计推断，其中行和列受到顺序限制。 所提出的估计过程基于Dykstra和Robertson（1982）为矩阵行和列的简单顺序限制开发的迭代算法。 对于矩阵行和列的任何顺序限制，推导出了算法在一次行和列操作应用中收敛的充分条件。 新算法适用于广泛的一类顺序限制。 在实践中，很容易设计一个研究，使得本文推导出的充分条件得到满足。 例如，在平衡设计中，充分条件得到满足。 使用本文开发的估计过程，提出了一个用于矩阵行和列顺序限制的Bootstrap检验。 对有序数据进行了计算机模拟，以大小和功效为指标，将所提出的检验与一些现有的检验程序进行比较。 通过将新方法应用于从毒理学研究中获得的一组有序数据来说明该新方法。 显示英文摘要

摘要： We present a general methodology for performing statistical inference on the components of a real-valued matrix parameter for which rows and columns are subject to order restrictions. The proposed estimation procedure is based on an iterative algorithm developed by Dykstra and Robertson (1982) for simple order restriction on rows and columns of a matrix. For any order restrictions on rows and columns of a matrix, sufficient conditions are derived for the algorithm to converge in a single application of row and column operations. The new algorithm is applicable to a broad collection of order restrictions. In practice, it is easy to design a study such that the sufficient conditions derived in this paper are satisfied. For instance, the sufficient conditions are satisfied in a balanced design. Using the estimation procedure developed in this article, a bootstrap test for order restrictions on rows and columns of a matrix is proposed. Computer simulations for ordinal data were performed to compare the proposed test with some existing test procedures in terms of size and power. The new methodology is illustrated by applying it to a set of ordinal data obtained from a toxicological study.