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.
|Commitee:||Benson, Chal, Brinkley, Jason, Said, Said E.|
|School:||East Carolina University|
|School Location:||United States -- North Carolina|
|Source:||MAI 48/05M, Masters Abstracts International|
|Keywords:||Brownian motion, Confidence intervals, Least concave majorant|
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