Statistical inference based on characteristic functions for intractable likelihood problems

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.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Statistics

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2018

Author dc:creator

• Yang, Fan

Contributors dc:contributor

• Chen, Yuguo
• Feng, Liming
• Chronopoulou, Alexandra
• Shao, Xiaofeng

• characteristic functions
• statistical inference
• Lévy processes
• MCMC
• trapezoidal rule
• asymptotic properties

Statement dc:rights

• Copyright 2018 Fan Yang

Language dc:language

en

Handle dc:identifier

http://hdl.handle.net/2142/101317

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/101317