Semiparametric Statistical Methods for Replicated Point Processes

University Of Wisconsin-Milwaukee, Milwaukee WI

Investigators

Abstract

The main goal of this project is the development of statistical tools for the analysis of points that occur at random in time or space, such as the locations of street robberies in a given city or the timings of spikes of neural activity for an individual performing a certain task. These data arise in many different fields including neuroscience, ecology, finance, astronomy, seismology, and criminology. The statistical methods to be developed under this project will then provide new data-analysis and inference tools for researchers and practitioners in diverse scientific fields. They will also be applicable to the analysis of data arising in strategic areas such as defense, public health and economy, thus contributing to the improvement of the well-being of individuals in society, the economic competitiveness of the United Stated, and national security. The educational activities related to this project, including the supervision of Ph.D. and Master's theses and the development of graduate and undergraduate Statistics courses, will also contribute to the improvement of graduate and undergraduate STEM education. In this project, semiparametric methods for estimation of the intensity functions of replicated point processes will be developed. In recent years, replicated point processes have become more common, and the possibility of pooling data across replications allows for the development of more efficient statistical methods. However, replicated point processes have received little attention in the Statistics literature and the methods to be developed under this project will help bridge that gap. The methods will be equally applicable to temporal or spatial processes, and will be developed for independent and identically distributed replications as well as for more complex dependency structures, such as ANOVA models, point processes with covariates, and multivariate processes. The research activities to be undertaken include the development of statistical models and parameter estimation methods, the development of algorithms and computer programs to implement these methods, the study of theoretical large sample properties, the study of small sample properties by simulation, and the analysis of real datasets.