Mathematical Sciences: Topics in Multivariate Survival Analysis and Counting Processes

该项目涉及三个主题：(1)多元分布和乘积积分的相关性和不对称性的概念：我们考虑一类互换性检验受审查的多变量随机向量。这些检验是基于对称化的风险函数，并从邻域中多元生存函数的乘积积分表示中得到它们的形式，这些邻域与可互换性假设相邻接。该项目的目的是开发这些测试的渐近性质。(2)马尔可夫更新过程估计和预测中的重采样方法：我们考察了两种不同的重采样方法来估计删失马尔可夫更新过程的更新矩阵，并将它们应用于设置置信度和预测区间。(3)加速失效时间模型中的L估计：在截尾截尾数据的半参数线性回归模型中推广了L估计。该项目的目的是在模型中开发新的推断方法，用于对医学、计量经济学和天文学等领域应用中产生的数据进行统计分析。将审议三个相互关联的主题，涉及检验假设、基于不完整数据的估计和预测。

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.