Advisor | Carolan, Christopher (Christopher A.) | en_US |
Author | Yang, Fan | en_US |
Date Accessioned | 2010-06-24T20:14:39Z | en_US |
Date Accessioned | 2011-05-17T15:04:42Z | |
Date Available | 2012-05-04T12:40:18Z | |
Date of Issue | 2010 | en_US |
Identifier (URI) | http://hdl.handle.net/10342/2798 | en_US |
Description | This thesis studies a new method to estimate the probability that a Brownian bridge crosses a concave boundary. We show that a Brownian bridge crosses a concave boundary if and only if its least concave majorant crosses said concave boundary. As such, we can equivalently simulate the least concave majorant of a Brownian bridge in order to estimate the probability that a Brownian bridge crosses a concave boundary. We apply these theoretical results to the problem of estimating joint confidence intervals for a true CDF at every point. We compare this method to a traditional method for estimating joint confidence intervals for the true CDF at every point which is based upon the limiting distribution of what is often called the Kolmogorov-Smirnov distance, the sup-norm distance between the empirical and true CDFs. We indicate the disadvantages of the traditional approach and demonstrate how our approach addresses these weaknesses. | en_US |
Extent | 46 p. | en_US |
Format Medium | dissertations, academic | en_US |
Language | en_US | en_US |
Publisher | East Carolina University | en_US |
Subject | Statistics | en_US |
Library of Congress Subject Headings | Gaussian processes | en_US |
Library of Congress Subject Headings | Brownian bridges (Mathematics) | en_US |
Title | ESTIMATION OF THE PROBABILITY A BROWNIAN BRIDGE CROSSES A CONCAVE BOUNDARY | en_US |
Type | Master's Thesis | en_US |
Department | Mathematics | en_US |
Degree | M.A. | en_US |