Statistical estimation of polynomial generalized covariance functions and hydrologic applications

Abstract

Minimum‐variance unbiased linear estimation theory has found many applications in the analysis of spatial rainfall and Hydrogeologic data: estimation of point values or areal averages, calculation of variances of estimation error, and network design. However, the important problem of inferring the spatial structure or interdependence of the function of interest has received relatively less attention. Three methods for the estimation of the parameters of Matheron's polynomial generalized covariance function (a useful model for nonstationary functions) are presented and evaluated: Maximum likelihood (ML), minimum variance unbiased quadratic (MVUQ), and minimum norm (least squares). The estimation error covariance matrix of the parameters is calculated with each of these methods. ML and MVUQ estimation have very good properties and, for reasonably large samples, give very similar results. Minimum norm estimation is appropriate for preliminary data analysis. The application of these methodologies is illustrated with a set of rainfall data, and problems of implementation are discussed. It is shown that the estimation of the parameters of the covariance function involves sizeable errors. It is suggested that, in practice, it may be rather difficult to identify the parameters of all but simple models. It is important that future research evaluate the effects of parameter uncertainty in the circulation of estimation error variances of point or areal averages and in the design of hydrologic data collection networks.

Cite this work

No public copy is stored for this record, so only the metadata is cited.

Stored only when both papers are in the corpus — 265 citations exist upstream.

Papers that cite the same references — the relational fallback while embeddings are still backfilling.