Dissertation/Thesis Abstract

Estimation of the probability a Brownian bridge crosses a concave boundary
by Yang, Fan, M.A., East Carolina University, 2010, 46; 1476637
Abstract (Summary)

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.

Indexing (document details)
Advisor: Carolan, Christopher
Commitee: Benson, Chal, Brinkley, Jason, Said, Said E.
School: East Carolina University
Department: Mathematics
School Location: United States -- North Carolina
Source: MAI 48/05M, Masters Abstracts International
Source Type: DISSERTATION
Subjects: Statistics
Keywords: Brownian motion, Confidence intervals, Least concave majorant
Publication Number: 1476637
ISBN: 978-1-124-01456-2
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