Dr. Scott Linder (Department of Mathematics and Computer Science)
In many practical settings, data are subjected to censoring, so that only some of the original subjects are observed. In Type I censoring, researchers will typically run an experiment for a predetermined length of time, and subjects still alive at the end of the experiment have failure times that have been censored. In Type II censoring, which typically arises by design, researchers observe a predetermined number of the original subjects before ending the experiment. For example, engineers might subject 100 metal rods to high pressures and record the failure times of the first 25 parts that fail. In this case, the failure times of the other 75 parts have been censored. Hence, with Type I censoring, the number of observations recorded is random, while with Type II censoring this number is fixed.
When data have been subjected to censoring the sampling distributions of statistics necessary for statistical modeling or inference are typically mathematically intractable and must be approximated. We examine the impact of censoring on these sampling distributions, develop methods for approximating the sampling distributions, and them examine the performance of inferential methods that may be extracted from them. For example, by approximating the sampling distribution of the sample correlation coefficient, it is possible to derive a confidence interval for the population correlation coefficient based on data arising from this kind of setting. The work involves an understanding of mathematical statistics, applied statistical modeling, computational simulation, and programming.