Estimator Stability in Geological Applications
Author: Shurygin, A.M.
Source: Mathematical Geology, Volume 32, Number 1, January 2000 , pp. 19-30(12)
Abstract:Classic mathematical statistics recommends maximum likelihood estimators of parameters of a model because they have minimal variance in the model. The theory of robustness showed that these estimators were unstable to small deviations of probability density. The estimator stability is necessary for applications, where reality is always more complex than any model, especially in geology, where objects are unique. Methods of calculus of variations give a measure of the estimator stability, and the maximum likelihood estimators have little stability. Simultaneous maximization of efficiency and stability gives new estimators more suitable for applications. The estimator instability is especially harmful in the estimation of the multivariate normal distribution. To avoid instability, multivariate problems are reduced to sequences of bivariate problems. An example of the solution of a geological problem shows that methods of classic statistics are not good and the reductive method is much better.
Document Type: Regular Paper
Affiliations: Department of Mechanics and Mathematics, Moscow State University, Moscow 119899, Russia; email@example.com
Publication date: January 1, 2000