Topics in Statistics with Applications

提案ID：0203798PI：智良英题：统计学与应用主题摘要本项目解决了与删失数据的半参数回归模型相关的问题，以及基于IRT的标准化测试所产生的项目差异功能的测试和估计。研究人员和他的合作者开发了新的算法来获得加速失效时间回归的参数估计器。这些算法都是基于线性规划的，易于实现。估计值是渐近正态的，极限方差通过简单的重采样方法估计。该方法被扩展到计量经济学文献中常见的删失分位数回归模型。他们通过估计方程来研究这类半参数变换模型，得到了一种通用的参数估计和推断方法，并得到了大样本理论的证明。他们开发了一种新的自适应标准化测试方法，通过带有测量误差的广义Logistic回归模型来检测可能的项目差异功能。这里讨论的统计问题的动机是生物医学、社会学、经济学、营销学、心理学和教育学的应用。该项目开发了适当的统计模型、计算机算法和数学理论。这些结果可以用来促进临床试验和流行病学研究的设计，特别是在癌症、心血管疾病和艾滋病的研究中，分析失业持续时间数据，量化消费者对营销策略的反应，并筛选出在大规模标准化测试中使用的项目，这些项目倾向于某个或多个群体，以确保公平

Proposal ID: 0203798PI: Zhiliang YingTitle: Topics in statistics with applicationsAbstractThis project addresses issues related to semiparametric regression models with censored data as well as testing and estimation of item differential functioning arising from IRT-based standardized tests. The investigator and his collaborators develop new algorithms for obtaining parameter estimators for the accelerated failure time regression. These algorithms are based on linear programming which is easy to implement. The estimators are shown to be asymptotically normal, with the limiting variance estimated via a simple resampling method. The approach is extended to censored quantile regression models, which are common in econometrics literature. They study the class of semiparametric transformation models via estimating equations, resulting in a general method for parameter estimation and inference, justified by a large sample theory. They develop a new approach for adaptive standardized tests to detect possible item differential functioning via a generalized logistic regression model with measurement errors. The statistical problems dealt with here are motivated by applications in biomedical sciences, sociology, economics, marketing, psychology and education. The project develops appropriate statistical models, computer algorithms and mathematical theory. The results can be used to facilitate design of clinical trials and epidemiological studies, particularly in studies of cancer, cardiovascular diseases and AIDS, to analyze unemployment duration data, to quantify consumer responses to marketing strategies and to screen out items for use in large-scale standardized tests that are tilted against certain group or groups to ensure fairness