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Title:Statistical inference based on characteristic functions for intractable likelihood problems
Author(s):Yang, Fan
Director of Research:Chen, Yuguo; Feng, Liming
Doctoral Committee Chair(s):Chen, Yuguo
Doctoral Committee Member(s):Chronopoulou, Alexandra; Shao, Xiaofeng
Department / Program:Statistics
Discipline:Statistics
Degree Granting Institution:University of Illinois at Urbana-Champaign
Degree:Ph.D.
Genre:Dissertation
Subject(s):characteristic functions
statistical inference
Lévy processes
MCMC
trapezoidal rule
asymptotic properties
Abstract:This dissertation is devoted to statistical inference based on characteristic functions. For some popular stochastic processes (e.g., Lévy processes, Lévy driven Ornstein-Uhlenbeck processes), the transition density may not be available. However, the (conditional) characteristic function is sometimes known. We study various statistical inference methods for fitting those processes with implicit characteristic functions. In the first part, an efficient sampling method based on Bayesian empirical likelihood is developed. The method involves pseudo-marginal Markov chain Monte Carlo with temperature and is shown to be effective for Lévy processes. In the second part and third part, we study maximum likelihood methods and empirical characteristic function estimation based on characteristic functions. We find the analyticity of the characteristic function can make efficient implementations of both methods possible, guaranteeing asymptotic properties as well. We also find, for certain models, very large samples might be needed to accurately identify the true parameters. Numerical results show the appealingness of some infinite activity models. In the last part, this dissertation includes my another project, which is about truth discovery in data mining. A dynamic model is developed to discover the truth between information sources across time. Experiments on real-world applications demonstrate its advantages over previous approaches.
Issue Date:2018-04-17
Type:Text
URI:http://hdl.handle.net/2142/101317
Rights Information:Copyright 2018 Fan Yang
Date Available in IDEALS:2018-09-04
Date Deposited:2018-05


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