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Point and confidence interval estimates for a global maximum via extreme value theory.
- Source :
- Journal of Applied Statistics; Dec2008, Vol. 35 Issue 12, p1371-1381, 11p, 4 Graphs
- Publication Year :
- 2008
-
Abstract
- The aim of this paper is to provide some practical aspects of point and interval estimates of the global maximum of a function using extreme value theory. Consider a real-valued function f:Dāī defined on a bounded interval D such that f is either not known analytically or is known analytically but has rather a complicated analytic form. We assume that f possesses a global maximum attained, say, at u*āD with maximal value x*=max u f(u)āf(u*). The problem of seeking the optimum of a function which is more or less unknown to the observer has resulted in the development of a large variety of search techniques. In this paper we use the extreme-value approach as appears in Dekkers et al. [A moment estimator for the index of an extreme-value distribution, Ann. Statist. 17 (1989), pp. 1833-1855] and de Haan [Estimation of the minimum of a function using order statistics, J. Amer. Statist. Assoc. 76 (1981), pp. 467-469]. We impose some Lipschitz conditions on the functions being investigated and through repeated simulation-based samplings, we provide various practical interpretations of the parameters involved as well as point and interval estimates for x*. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 02664763
- Volume :
- 35
- Issue :
- 12
- Database :
- Complementary Index
- Journal :
- Journal of Applied Statistics
- Publication Type :
- Academic Journal
- Accession number :
- 34716580
- Full Text :
- https://doi.org/10.1080/02664760802382442