Detection of bumps on the intensity function of an inhomogeneous Poisson process
Abstract/Contents
- Abstract
- The Scanning Statistics methodology has been applied to problems arising in many disciplines including epidemiology and genomics. In this thesis we propose a modification of the Scan Statistic for the Poisson model and we compare it with other tests based on this methodology. Poisson Processes have been widely used in credit risk to build models of credit defaults across time. Despite this, few papers are focused on building tools to test these models. In this thesis we use Scanning Statistics to test a particular family of credit risk models. We haven't seen an application of Scanning Statistics to credit risk. We consider the inhomogeneous Poisson Process with intensity p[mu](t) on an interval I and q[mu](t) on [0,1]\I. Suppose that the intensity [mu](t) is known while p, q and I are un- known. This problem can be transformed into detecting clusters on a sample of iid uniform random variables. We use scanning statistics to approach these problems and propose a scale penalty for the Scan (Maximum Likelihood Ratio Test). We establish detection conditions for this penalized test and also study the power of the Average Maximum Likelihood Ratio Test.
Description
| Type of resource | text |
|---|---|
| Form | electronic; electronic resource; remote |
| Extent | 1 online resource. |
| Publication date | 2012 |
| Issuance | monographic |
| Language | English |
Creators/Contributors
| Associated with | Rivera Guerrero, Camilo Andres |
|---|---|
| Associated with | Stanford University, Department of Statistics |
| Primary advisor | Walther, Guenther |
| Thesis advisor | Walther, Guenther |
| Thesis advisor | Taylor, Jonathan E |
| Thesis advisor | Zhang, Nancy R. (Nancy Ruonan) |
| Advisor | Taylor, Jonathan E |
| Advisor | Zhang, Nancy R. (Nancy Ruonan) |
Subjects
| Genre | Theses |
|---|
Bibliographic information
| Statement of responsibility | Camilo Rivera. |
|---|---|
| Note | Submitted to the Department of Statistics. |
| Thesis | Thesis (Ph.D.)--Stanford University, 2012. |
| Location | electronic resource |
Access conditions
- Copyright
- © 2012 by Camilo Andres Rivera Guerrero
- License
- This work is licensed under a Creative Commons Attribution Non Commercial 3.0 Unported license (CC BY-NC).
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