Akimichi Takemura (Faculty of Economics, University of Tokyo.) Satoshi Kuriki (The Institute of Statistical Mathematics)
Abstract
Consider a Gaussian random field Z(u) with mean 0, variance 1, and finite Karhunen-Loeve expansion. Under a very general assumption that the index set M is a manifold with piecewise smooth boundary, we prove the validity and the equivalence of two currently available methods for obtaining the asymptotic expansion of tail probability of the maximum of Z(u). One is the tube method, where the volume of tube around the index set M is evaluated. The other is the Euler characteristic method, where the expectation for the Euler characteristic of excursion set is evaluated. In order to show this equivalence we prove a version of the Morse's theorem for a manifold with piecewise smooth boundary. These results on the tail probabilities are generalizations of those of Takemura and Kuriki (1997), where M was assumed to be convex.
Download Info
To download:
If you experience problems downloading a file, check if you have the
proper application to
view it first. Information about this may be contained
in the File-Format links below. In case of further problems read
the IDEAS help
page. Note that these files are not on the IDEAS
site. Please be patient as the files may be large.
Publisher Info
Paper provided by CIRJE, Faculty of Economics, University of Tokyo in its series CIRJE F-Series with number
CIRJE-F-54.
References listed on IDEAS Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
Cited by: (explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)