Nonparametric maximum likelihood estimation of spatial patterns. Technical report No. 29
Let X be an absolutely continuous random variable in R/sup k/ with distribution function F(x) and density f(x). Let X/sub 1/,..., X/sub n/ be independent random variables distributed according to F. Mapping the spatial distribution of X normally entails drawing a map of the isopleths, or level curves, of f. This paper shows how to map the isopleths of f nonparametrically according to the criterion of maximum likelihood. The procedure involves specification of a class L of sets whose boundaries constitute admissible isopleths and then maximizing the likelihood PI/sub i = 1//sup n/g(x/sub i/) over all g whose isopleths are boundaries of L-sets. The only restrictions on L are that it be a sigma-lattice and an F-uniformity class. The computation of the estimate is normally straightforward and easy. Extension is made to the important case where L may be data-dependent up to locational and/or rotational translations. Strong consistency of the estimator is shown in the most general case.
- Research Organization:
- Stanford Univ., CA (USA). Dept. of Statistics
- DOE Contract Number:
- EY-76-S-02-2874
- OSTI ID:
- 5500110
- Report Number(s):
- DOE/EY/22874-60
- Country of Publication:
- United States
- Language:
- English
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