Large Deviations for the Maxima of Some Random Fields.
STANFORD UNIV CA DEPT OF STATISTICS
Pagination or Media Count:
Several statistical problems which involve the distribution of the maximum of Gaussian random fields are described. Specific examples are the pinned Brownian sheet and a Brownian bridge with reflection, which arises in certain change point problems. In these concrete cases the method of Pickands 1969, Trans. Amer. Math. Soc. is adapted to give large deviation probabilities for the maximum, both for continuous and for discrete indexing sets. A different method is used to give a second order correction for the reflected Brownian bridge and hence for reflected Brownian motion. The numerical accuracy of the approximations is studied via simulation.
- Statistics and Probability