Collecting spatial data. Optimum design of experiments for random fields.
type: Item
instance of: scholarly article
title: Collecting spatial data. Optimum design of experiments for random fields.
zbMATH Open document ID: 0972.62050
author: Werner G. Müller
published in: Contributions to Statistics
publication date: 2000-11-30T00:00:00Z
review text: Spatial data have the distinctive characteristic that, attached to every observation, we have a set of coordinates that identifies the (geographical) position of a respective data collection site. The set of locations of those data collection sites (the so-called design) influences the quality of the results of the statistical analysis. Sampling theory and optimum experimental design theory are two large branches of theoretical statistics that provide methods for efficient site positioning. Whereas sampling theory is a basically model-free methodology essentially oriented towards restoring unobserved data, in optimum design theory the aim is to estimate the structure of the data generating process, e.g., the parameters of an assumed (regression) model or functions of these parameters. In this monograph emphasis is on the latter branch. Principles from optimum design theory are used in adapting and developing methods specific for the solution of the spatial design problem. In Chapter 2, a short overview on the predominant geostatistical techniques is given. Estimation techniques for parameters of measures of both first (mean, trend) and second order characteristics (variogram, spatial covariance function) are reviewed. Universal kriging is presented as a special form of generalized least squares estimation. A well-known nonparametric estimation method, the local regression technique, is shown to be a useful complement to kriging. Some of its properties, that are relevant in the spatial setting, are derived. Kriging requires parametric variogram estimation. It is indicated that the most frequently applied (weighted least squares) estimator is generally inconsistent and remedies for this problem are suggested. Chapter 3 contains a description of the basic principles of optimum experimental design theory. Here optimality refers to a prespecified criterion such as the minimization of the variances of the estimates. Emphasis is again on aspects that are particularly relev…
Mathematics Subject Classification ID: 62K05
Mathematics Subject Classification ID: 62M30
Mathematics Subject Classification ID: 62-02
Mathematics Subject Classification ID: 62M40
Mathematics Subject Classification ID: 62P12
zbMATH DE Number: 1537376
zbMATH Keywords: kriging
zbMATH Keywords: parametric estimation
zbMATH Keywords: variogram
zbMATH Keywords: weighted least squares
zbMATH Keywords: minimax distance designs
zbMATH Keywords: information matrix
reviewed by: M. P. Moklyachuk
describes a project that uses: GAUSS
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1537376