ESTIMATION OF THE PROBABILITY A BROWNIAN BRIDGE CROSSES A CONCAVE BOUNDARY
- ECU Author/Contributor (non-ECU co-authors, if there are any, appear on document)
- FAN YANG (Creator)
- East Carolina University (ECU )
- Web Site: http://www.ecu.edu/lib/
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.
- Language: English
- Date: 2010
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|ESTIMATION OF THE PROBABILITY A BROWNIAN BRIDGE CROSSES A CONCAVE BOUNDARY||http://thescholarship.ecu.edu/bitstream/handle/10342/2798/YANG_ecu_0600M_10127.pdf||The described resource references, cites, or otherwise points to the related resource.