Statistical inference based on characteristic functions for intractable likelihood problems

Yang, Fan

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https://hdl.handle.net/2142/101317 Copy

Description

Title

Statistical inference based on characteristic functions for intractable likelihood problems

Author(s)

Yang, Fan

Issue Date

2018-04-17

Director of Research (if dissertation) or Advisor (if thesis)

• Chen, Yuguo
• Feng, Liming

Doctoral Committee Chair(s)

Chen, Yuguo

Committee Member(s)

• Chronopoulou, Alexandra
• Shao, Xiaofeng

Department of Study

Statistics

Discipline

Statistics

Degree Granting Institution

University of Illinois at Urbana-Champaign

Degree Name

Ph.D.

Degree Level

Dissertation

Keyword(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.

Graduation Semester

2018-05

Type of Resource

text

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

Copyright and License Information

Copyright 2018 Fan Yang

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