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Approximate Tail Probabilities for the Maxima of Some Random Fields
STANFORD UNIV CA DEPT OF STATISTICS
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Hogan and Siegmund 1986 adapt the method developed by Pickands 1969, Qualls and Watanabe 1973, and Bickel and Rosenblatt 1973 to obtain explicit large deviation approximations for the maxima of several Gaussian random fields arising in statistics. Using a special argument for one particular case, they suggest a heuristic second order approximation for that case and they show by a Monte Carlo experiment that the second order approximation frequently gives considerably better numerical results. The purpose of this paper is to show that the method developed by Woodroofe 1976,1982 for problems in one dimensional time can be adapted to study maxima of random fields. Overall it involves simpler computations than the previous method and consequently seems potentially capable of delivering a genuine second order approximation should one seem desirable.
APPROVED FOR PUBLIC RELEASE