Estimation in exponential families with unknown normalizing constant
- Exponential families of probability measures has been a subject of considerable interest in Statistics, both in theoretical and applied areas. One of the problems that frequently arise in such models is that the normalizing constant is not known in closed form. Also numerical computation of the normalizing constant is infeasible because the size of the underlying space is huge. As such, carrying out inferential procedures becomes challenging. In this thesis, the main object of study is some specific examples of exponential families on graphs and permutations, where the normalizing constant is hard to compute. Using large deviation results asymptotic estimates of the normalizing constant is obtained, and methods to estimate the normalizing constant are developed. In the case of graphs, this analysis gives some insight into the phenomenon of "degeneracy" observed in empirical studies in social science literature. In the case of permutations, this analysis is used to show the consistency of pseudo-likelihood.
|Type of resource
|electronic; electronic resource; remote
|1 online resource.
|Stanford University, Department of Statistics.
|Statement of responsibility
|Submitted to the Department of Statistics.
|Thesis (Ph.D.)--Stanford University, 2014.
- © 2014 by Sumit Mukherjee
- This work is licensed under a Creative Commons Attribution Non Commercial 3.0 Unported license (CC BY-NC).
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