UC Riverside

Combining multiple tests has many real world applications. However, most existing methods fail to directly take into account the underlying dependency among the tests. In the first project of this dissertation, we propose a novel procedure to combine dependent tests based on the notion of data depth. The proposed method can automatically incorporate the underlying dependency among the tests, and is nonparametric and completely data-driven. To demonstrate its application, we apply the proposed combining method to develop a new two-sample test for data of arbitrary types when the data can be metrizable and their information can be characterized by interpoint distances. Our simulation studies and real data analysis show that the proposed test based on the new combining method performs well across a broad range of settings and compares favorably with existing tests.

Count data monitoring has important applications in many fields. However, most of the existing control charts for monitoring count data are parametric. Parametric control charts can be problematic when the underlying parametric distributional assumption does not hold for the particular application. On the other hand, nonparametric control charts do not require such distributional assumptions, and are more desirable in real-world situations where the underlying distribution cannot be easily described using a parametric distribution. In the second project of this dissertation, we extend the nonparametric control chart for continuous data monitoring in Li (2021) to count data monitoring. To guarantee a desired in-control performance, we further adopt the bootstrap procedure from Gandy and Kvaløy (2013) to help determine the control limit of our proposed control chart. Our simulation studies and real data analysis show that the proposed control chart performs well across a variety of settings, and compares favorably with other existing nonparametric control charts for count data.