Colloquium: Consistent and Inconsistent Estimation in Geostatistics
4:35 p.m. Neill Hall 5W
Abstract: Geostatistics is composed of tools for collecting and analyzing those spatial data that are sampled in a continuous spatial region. It has its origin in mining but has become an integral part of statistics due to the work of some mainstream statisticians in the past few decades. This talk will cover some recent theoretical advances and their applications to spatial data analysis. In particular, we will show that most parameters in some common models for the covariance function of a stationary process are not consistently estimable, if data are collected in a fixed region. However, some functions of the parameters are consistently estimable and these functions have a greater impact on interpolation than each individual parameter. We will establish the strong consistency of the maximum likelihood estimators of these functions. Properties of equivalent probability measures are used in the proofs. We will present simulation results to discover the meanings of consistency and inconsistency in finite sample cases. Part of the talk is from the recently accepted paper in JASA (Zhang, 2003. http://www.stat.wsu.edu/personal/homepage/zhang/Paper/JASA02-198.pdf).