Inference for Dynamic Objects

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Modern data collection techniques result in a steady stream of complex data. The field of statistics has an obligation to develop tools for their analysis, allowing users to draw meaningful and correct conclusions. In view of the complexity of the collected data, this is a challenging task. This project will tackle these challenges by not only constructing relevant novel methodologies, but by also analyzing these methods in order to establish a thorough understanding of their strengths and weaknesses. This, in turn, will facilitate an honest evaluation and interpretation of practical data analysis results. One instance of a complex data type considered in this project is network data. A relevant real-world example is the world trade network, consisting of trading indices between pairs of countries. Countries can be grouped into trading blocks, and this project will develop methodology allowing the analysis of the dependence structure between the trading blocks. This will help to identify factors that are driving this dependence, and how they change over time. More generally, the outcomes of this project are expected to impact the field of statistics and various fields of application. This will be achieved by widely disseminating statistical insight, methodologies and theory developed in this project through publications in international statistics journals, presentations at national and international conferences, and by developing relevant software/code to be made available to the community. Moreover, this project will directly contribute to the training of both graduate students and undergraduate students in modern fields of statistics. It is expected that there will be mutual benefits and synergies between this project and the ongoing NSF Research Training Grant in Statistics at UC Davis. This project seeks to develop novel statistical methods for the analysis of dynamic object data, in particular, networks and functional data. More specifically, this project will (i) study dependence structures in hierarchical time-varying block models for stochastic networks, and apply the resulting methodologies to the analysis of economic network data such as trade networks; (ii) develop a class of continuous-time point process models for random networks, allowing for a flexible model and analysis of the corresponding maximum likelihood estimators in these models; (iii) develop empirical likelihood based inference methodology for functional time series. The project aims at developing methodologies that, on the one hand, are flexible enough and computationally feasible to be useful for complex real-world applications, and that, on the other hand, result in methodologies that allow rigorous statistical analyses providing insight into, and understanding of, their behavior.