Estimation of the Probability a Brownian Bridge Crosses a Concave Boundary
Author | : Fan Yang |
Publisher | : |
Total Pages | : 46 |
Release | : 2010 |
ISBN-10 | : OCLC:648765096 |
ISBN-13 | : |
Rating | : 4/5 (96 Downloads) |
Download or read book Estimation of the Probability a Brownian Bridge Crosses a Concave Boundary written by Fan Yang and published by . This book was released on 2010 with total page 46 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.