自变量受限的回归模型的同步置信带

项目名称： 自变量受限的回归模型的同步置信带

项目编号： No.11201059

项目类型： 青年科学基金项目

立项/批准年度： 2013

项目学科： 数理科学和化学

项目作者： 蔺杉

作者单位： 东北师范大学

项目金额： 22万元

中文摘要： 置信带的研究一直都是统计学中一个重要的推断问题。相对于置信区间，置信带不仅具有更优越的多元统计意义，更具有良好的应用前景。置信带提供了真实回归模型均值的位置信息，可用于检验某个给定的方程可否作为样本数据合理的回归表达。然而，人们发现当自变量增多或者取值受限时，置信带的构建成为了一个难题。本项目要研究的是在实际问题中经常出现的矩形自变量限制区域上构建非精确置信带的方法，以及通过统计模拟展现相关方法的实际运算能力。针对模型非线性的情形，选取广义线性模型为研究对象，通过比较模拟的置信带覆盖概率和预设置信水平来考察几种非精确置信带的精度。此外，针对市场营销中Logit模型的广泛应用，我们还将特别地讨论对于Logit模型置信带相关的构建问题。

中文关键词： 置信带；线性回归；多项式回归；广义线性模型；

英文摘要： Research on simultaneous confidence bands has always been an important statistical inference problem. Compared to confidence intervals, confidence bands not only has superior multivariate statistical significance, but also has good applicable prospects. A confidence band provides the location information of the true regression mean and can be used to test if a given function can be viewed as a reasonable candidate of the real model based on sample data. However, it's found that construction of confidence bands becomes a hard problem when the number of predictor variables is increased or the domains of predictor variables are restricted. This project is to work on non-exact construction methods of confidence bands over rectangular predictor space which often appears in practical problems, and compare the performances of involved methods in various data environments via statistical simulations. As for models non-linear situations, we shall select the generalized linear models for studying, to check the accuracies of the non-exact confidence bands by comparing the simulated bands' coverage probabilities to the pre-assigned confidence levels.In addition, we shall particularly discuss some issues on constructing confidence bands for Logit models due to their wide uses in marketing science.

英文关键词： Simultaneous confidence bands；Linear regression；Polynomial regression；Generalised linear model；