标题： 对多项分布相等性的检验与递增凸序 显示英文标题

标题： A test for equality of multinomial distributions vs increasing convex order

摘要： 最近，刘和王推导了用于检验两个多项分布相等性的似然比检验（LRT）统计量及其渐近分布，相对于备择假设，即第二个分布在增加凸序（ICX）方面更大。 ICX比随机秩序更不严格，并且是一个在保险和精算科学中已找到应用的概念。 在本文中，我们提出了一个针对ICX的新检验。 该新检验在多个方面优于LRT以及任何依赖于渐近理论进行实施的检验程序。 优点包括以下几点：(i) 该检验是精确的（非渐近的）。 (ii) 该检验通过在边缘列总计上进行条件分析（在完整多项式模型中的$2\times C$表中还包括行总计）。 (iii) 该检验具有理想的单调性特性。 也就是说，该检验在所有实际方向上都是单调的（将被正式定义）。 (iv) 该检验可以通过计算机程序的帮助进行计算。 (v) 该检验在各种可能的替代方案中具有良好的功效特性。 (vi) 该检验是可接受的。 新检验的基础是Cohen、Madigan和Sackrowitz开发的定向卡方方法。 显示英文摘要

摘要： Recently Liu and Wang derived the likelihood ratio test (LRT) statistic and its asymptotic distribution for testing equality of two multinomial distributions vs. the alternative that the second distribution is larger in terms of increasing convex order (ICX). ICX is less restrictive than stochastic order and is a notion that has found applications in insurance and actuarial science. In this paper we propose a new test for ICX. The new test has several advantages over the LRT and over any test procedure that depends on asymptotic theory for implementation. The advantages include the following: (i) The test is exact (non-asymptotic). (ii) The test is performed by conditioning on marginal column totals (and row totals in a full multinomial model for a $2\times C$ table). (iii) The test has desirable monotonicity properties. That is, the test is monotone in all practical directions (to be formally defined). (iv) The test can be carried out computationally with the aid of a computer program. (v) The test has good power properties among a wide variety of possible alternatives. (vi) The test is admissible. The basis of the new test is the directed chi-square methodology developed by Cohen, Madigan, and Sackrowitz.