Contributions to Nonparametric Predictive Inference with Right-Censored Data

A right-censored data set is most common in reliability and survival analyses. It occurs when a particular event of interest is not fully observed in an experiment and when there is no information provided about a random quantity except that it exceeds a certain value. Nonparametric Predictive Inference (NPI) is a frequentist statistical method based on only few assumptions. It focuses explicitly on future observations and uses imprecise probabilities, based on Hill's assumption A(n), to quantify uncertainty. NPI has been developed for several types of data, including right-censored data. However, NPI with right-censored data has only taken into consideration a single future observation. This thesis presents three contributions to NPI with right-censored data. First, some statistical methods on extreme values assume that the endpoint of the support is equal to the largest observed value in a data set. However, a question that may be of interest is whether, for some right-censored observations in a data set, their actual value might exceed the largest observed value. Secondly, the actuarial estimator provides information on the number of events and censorings at any given discrete point in time. The nature of this estimator is such that, at every time point (except if all people in the data set have died) there is right-censoring, the data themselves are not necessarily right-censored. A similar approach is followed here, but we aim to develop an alternative method to the actuarial estimator, based on NPI with right-censored data. The proposed method will be used to derive NPI lower and upper probabilities for a variety of events of interest. As an example application, we apply the newly developed method to obtain NPI lower and upper survival probabilities for reliability of systems. Thirdly, NPI has been developed for real-valued data that contain right-censored observations but only a single future observation was considered. There may be reasons to be interested in multiple future observations, and it is important that in the NPI approach such multiple future observations are not conditionally independent given the data. We extend NPI for right-censored data by considering two future observations. Particularly, we present NPI lower and upper probabilities for the event that both future observations are greater than time t. We apply the proposed method to system reliability. The results in this thesis widen the applicability of NPI for several real-world scenarios, while also suggesting new related topics for research.