Statistical validation of rival models for observable stochastic process and its identification

N. Nechval, M. Purgailis, K. Nechval
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Abstract

In this paper, for statistical validation of rival (analytical or simulation) models collected for modeling observable process in stochastic system (say, transportation or service system), a uniformly most powerful invariant (UMPI) test is developed from the generalized maximum likelihood ratio (GMLR). This test can be considered as a result of a new approach to solving the Behrens-Fisher problem when covariance matrices of multivariate normal populations (compared with respect to their means) are different and unknown. The test makes use of an invariant statistic whose distribution, under the null hypothesis, does not depend on the unknown (nuisance) parameters. The sample size and threshold of the UMPI test are determined from minimization of the weighted sum of the model builder's risk and the model user's risk. The rules are proposed to identify an observable process with one of several rival models, suitable for modeling, which accurately represents the process, especially when decisions involving expensive resources are made on the basis of the results of the model. Application examples are given.
可观测随机过程竞争模型的统计验证及其辨识
本文从广义最大似然比(GMLR)出发,对随机系统(如运输或服务系统)中可观测过程建模所收集的竞争(分析或模拟)模型进行了统计验证,提出了统一最强大不变量(UMPI)检验。当多元正态总体的协方差矩阵(相对于其均值)不同且未知时,可以将此检验视为解决Behrens-Fisher问题的新方法的结果。该检验使用不变统计量,其分布在零假设下不依赖于未知(干扰)参数。UMPI测试的样本量和阈值是通过最小化模型构建者风险和模型用户风险的加权和来确定的。提出的规则是用几个适合建模的竞争模型中的一个来识别可观察过程,该模型准确地表示该过程,特别是当基于模型的结果做出涉及昂贵资源的决策时。给出了应用实例。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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