An excursion approach to maxima of the Brownian bridge.

Stoch Process Their Appl

Department of Statistics, University of Washington, B320 Padelford Hall, Seattle, WA 98195-4322, USA.

Published: September 2014

AI Article Synopsis

  • The paper talks about how certain types of math related to Brownian bridges (a fancy kind of graph) help in statistics without specific formulas.
  • It explains how to find the highest or lowest points on the Brownian bridge using a method called excursion theory.
  • They also show how their new way of looking at things can help explain some familiar statistics, like the Kolmogorov-Smirnov and Kuiper statistics, and even uncover some new ones!

Article Abstract

Distributions of functionals of Brownian bridge arise as limiting distributions in non-parametric statistics. In this paper we will give a derivation of distributions of extrema of the Brownian bridge based on excursion theory for Brownian motion. The idea of rescaling and conditioning on the local time has been used widely in the literature. In this paper it is used to give a unified derivation of a number of known distributions, and a few new ones. Particular cases of calculations include the distribution of the Kolmogorov-Smirnov statistic and the Kuiper statistic.

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Source
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC4847753PMC
http://dx.doi.org/10.1016/j.spa.2014.04.008DOI Listing

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