Approximate Tail Probabilities for the Maxima of Some Random Fields
Abstract
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.
Document Details
- Document Type
- Technical Report
- Publication Date
- Aug 01, 1986
- Accession Number
- ADA172729
Entities
People
- David Siegmund
Organizations
- Stanford University