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    ESTIMATION OF THE PROBABILITY A BROWNIAN BRIDGE CROSSES A CONCAVE BOUNDARY

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    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.  
    URI
    http://hdl.handle.net/10342/2798
    Subject
    Statistics
    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.)

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    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. July 06, 2022.
    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
    • Master's Theses
    • Mathematics
    Publisher
    East Carolina University

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