Mathematical Sciences: Topics in Multivariate Survival Analysis and Counting Processes

本课题涉及三个主题：(1)多元分布与积积分的依赖与不对称概念；考虑了一类多变量随机向量可交换性的检验。这些检验基于对称的危险函数，并从邻近可交换性假设的多变量生存函数的积积分表示中推导出它们的形式。该项目的目的是发展这些检验的渐近性质。(2)马尔可夫更新过程估计和预测的重采样方法：研究了两种不同的马尔可夫更新过程估计更新矩阵的重采样方法，并将其应用于置信度和预测区间的设置。(3)加速失效时间模型中的l -估计：在截断和截短数据的半参数线性回归模型中，对l -估计进行了推广。该项目的目的是在为医学、计量经济学和天文学等领域的应用中产生的数据进行统计分析而设计的模型中发展新的推理方法。将考虑三个相互关联的主题，并将处理基于不完整数据的测试假设，估计和预测。

The project concerns three topics: (1) Concepts of dependence and asymmetry of multivariate distributions and product integrals: we consider a class of tests for exchangeability of multivariate random vectors subject to censoring. The tests are based on symmetrized hazard functions and derive their form from the product integral representation of multivariate survival functions in neighborhoods contiguous to the hypothesis of exchangeability. The aim of the project is to develop asymptotic properties of these tests. (2) Resampling methods in estimation and prediction from Markov renewal processes: we examine two different resampling methods in estimation of the renewal matrix from a censored Markov renewal process and apply them towards setting confidence and prediction intervals. (3) L-estimation in the accelerated failure time model: we develop an extension of L-estimates in a semiparametric linear regression model with censored and truncated data. The aim of the project is to develop new inference methods in models designed for statistical analysis of data arising in application to areas such as medicine, econometrics and astronomy. Three interrelated topics will be considered and will deal with testing hypotheses, estimation and prediction based on incomplete data.