Testing invariance for random field modeling
The application of the collocation theory to the prediction of some random field functional depends on the knowledge of the covariance function. Whether we include the estimation of the covariance into a unique theoretical set up with the prediction of the signal, or we do it separately in a more traditional way, this step can be performed only under the assumption of some stochastic invariance of the field; under such a hypothesis, in fact, we can use a single sample to estimate the empirical covariance function.
However one easily realizes that the empirical estimator provides numerical answers even if applied to signals whose stochastic invariance is out of question. This calls for some criterion to decide, at least a posteriori, whether the hypothesis, on which the covariance estimation is based, is likely to be true or not.
Three different testing procedures were considered and applied to simulated data. The results obtained are discussed in the paper; they lead to a procedure, at least in a simplified context, which verifies whether the sample has or does not have a deterministic linear trend.
A more general result is finally presented, namely how to retrieve an estimate of the empirical covariance function of the signal, correcting the one estimated on the residues of the linear regression.
KeywordsCovariance estimate invariance hypothesis testing procedures
Unable to display preview. Download preview PDF.
- Box, G.E.P. and G. Jenkins (1976). Time Series Analysis: Forecasting and Control. Holden-Day, San Francisco.Google Scholar
- Cox, D.R. and D.V. Hinkley (1974). Theoretical Statistics. Chapman and Hall, London.Google Scholar
- Moritz, H. (1989). Advanced Physical Geodesy. Wichmann, Karlsruhe.Google Scholar
- Sachs, L. (1982). Applied Statistics. A Handbook of Techniques. Springer-Verlag, New York.Google Scholar
- Sans?), F. (1986). Statistical Methods in Physical Geodesy. In: Mathematical and Numerical Techniques in Physical Geodesy,Lecture Notes in Earth Sciences, Vol. 7, Springer-Verlag, Berlin, pp. 49–155.Google Scholar
- Wackernagel, H. (1995). Multivariate Geostatistics. Springer-Verlag, Berlin.Google Scholar