Inference in the statistical models for counting processes information with incomplete data and studies of three types of partial likelihoods

我们考虑统计推断的方法，以便从跟踪时间收集的数据中确认或发现正在调查的科学知识，这些时间是抽样或从人群中选择的个体经历感兴趣的事件的时间。然后，如果观察到的数据包含个体的不确定伴随信息，则发现至少有三种基于数学科学观点的统计推断方法。我们研究了这三种类型在科学中是否真正有效，以及这三种类型之间是如何相互关联的，从而我们可以得到一些有用的发现，关于数学科学的贡献和在实质性科学领域的应用。

We consider methods for statistical inference in order to confirm or discovery a scientific knowledge under investigation from the data collected by following up times at which individuals sampled or selected from the population experience the event of interest. Then, if the observed data include uncertain concomitant information for individuals, it is founded that there are at least three types of statistical inference methods, based on outlooks in mathematical science. We studied whether the 3-types are truly valid methods in science, and how the 3-types are related to each other, so that we could obtain several useful findings on contributions in mathematical science and applications to substantial science fields.