Mathematical Sciences: Topics in Multivariate Survival Analysis and Counting Processes

该项目涉及三个主题： (1)多变量的相关性和不对称性概念 分布和积积分：我们考虑一个 多元互换性检验类 随机向量进行审查。 该测试基于对称化的风险函数， 从积积分导出它们的形式 多元生存函数的表示 邻近的假设， 交换该项目的目的是开发 这些测试的渐近性质。 (2)估计和预测中的恢复方法 马尔可夫更新过程：我们研究两个不同的 更新矩阵估计的一种改进方法 从一个截尾马尔可夫更新过程，并应用它们 设定置信区间和预测区间。 (3)加速失效时间模型中的L-估计 半参数L-估计的推广 截尾线性回归模型 数据 该项目的目的是开发新的推理 用于统计分析的模型中的方法 在应用于诸如医学等领域时产生的数据， 计量经济学和天文学。 三个相互关联的主题 将被考虑，并将处理测试 假设、估计和预测， 数据不完整。

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.