Department of Statistics Seminar
North Carolina State University

presents

Marc G. Genton

Massachusetts Institute of Technology

"On the Robustness Properties of Variogram Estimators and their Fit"

ABSTRACT

Variogram estimation and fitting are two crucial stages of spatial prediction. Because they determine the kriging weights, they must be carried out carefully. Otherwise kriging can produce non-informative maps. The classical variogram estimator proposed by Matheron is not robust against outliers in the data, nor is it enough to make simple modifications such as the ones proposed by Cressie and Hawkins in order to achieve robustness. A new variogram estimator based on a highly robust estimator of scale is proposed. The robustness properties of these three estimators are analyzed by means of the influence function and the classical breakdown point. The latter is extended to a spatial breakdown point, which depends on the construction of most unfavorable configurations of perturbation. Variogram estimates at different spatial lags are correlated, for the same observation is used for different lags. The correlation structure of variogram estimators is analyzed for Gaussian data, and then extended to elliptically contoured distributions. Its use for variogram fitting by generalized least squares is presented. Simulations are carried out with several types of underlying variograms, as well as with outliers in the data. Results show that our techniques improve the estimation and the fit significantly. Finally, these robust methods are applied on a data set of sediments from Lake Geneva in Switzerland, using the software S+SpatialStats extended with some new functions in Splus.

Friday, April 3, 1998

3:35 - 4:35 pm

206 Cox Hall

Refreshments will be served on the second floor of Dabney Hall (left of Room 222) at 3:00 pm.