ESTIMATION OF THE PROBABILITY A BROWNIAN BRIDGE CROSSES A CONCAVE BOUNDARY
Author
Yang, Fan
Abstract
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.
Subject
Date
2010
Citation:
APA:
Yang, Fan.
(January 2010).
ESTIMATION OF THE PROBABILITY A BROWNIAN BRIDGE CROSSES A CONCAVE BOUNDARY
(Master's Thesis, East Carolina University). Retrieved from the Scholarship.
(http://hdl.handle.net/10342/2798.)
MLA:
Yang, Fan.
ESTIMATION OF THE PROBABILITY A BROWNIAN BRIDGE CROSSES A CONCAVE BOUNDARY.
Master's Thesis. East Carolina University,
January 2010. The Scholarship.
http://hdl.handle.net/10342/2798.
September 21, 2023.
Chicago:
Yang, Fan,
“ESTIMATION OF THE PROBABILITY A BROWNIAN BRIDGE CROSSES A CONCAVE BOUNDARY”
(Master's Thesis., East Carolina University,
January 2010).
AMA:
Yang, Fan.
ESTIMATION OF THE PROBABILITY A BROWNIAN BRIDGE CROSSES A CONCAVE BOUNDARY
[Master's Thesis]. Greenville, NC: East Carolina University;
January 2010.
Collections
Publisher
East Carolina University