@article{JARMOŁOWSKI_BAKUŁA_2013, title={Two covariance models in Least Squares Collocation (LSC) tested in interpolation of local topography}, volume={43}, url={https://journal.geo.sav.sk/cgg/article/view/83}, DOI={10.2478/congeo-2013-0001}, abstractNote={<p>Advantages and disadvantages of least squares collocation (LSC) and kriging<br>have recently been discussed, especially as interdisciplinary research becomes popular.<br>These statistical methods, based on a least squares rule, have infinite number of applications,<br>also in the domains different than Earth sciences. The paper investigates covariance<br>parameters estimation for spatial LSC interpolation, via a kind of cross-validation, called<br>hold-out (HO) validation. Two covariance models are applied in order to reveal also those<br>differences that come solely from the covariance model.<br>Typical covariance models have a few variable parameters, the selection of which requires<br>analysis of the actual data distribution. Properly chosen covariance parameters<br>result in accurate and reliable predictions. The correlation length (CL), also known as<br>the correlation distance in the Gauss-Markov covariance functions, the variance (C0) and<br>a priori noise parameter (N) are analyzed in this paper, using local terrain elevations.<br>The covariance matrix is used in LSC, as analogy to the correlation matrix often present<br>in the kriging-related investigations. Therefore the covariance parameter N has the same<br>scale as the data and can be analyzed in relation to the data errors, spatial data resolution<br>and prediction errors.<br>The vector of the optimal three covariance parameters is sometimes determined approximately<br>for the purposes of modeling with limited accuracy requirements. This is<br>done e.g. by the fitting of analytical model to the empirical covariance values. The more<br>demanding predictions need precise estimation of the covariance parameters vector and<br>the researchers solve this problem via least squares methods or maximum likelihood (ML)<br>inference. Nevertheless, both least squares and ML produce an error of the parameters<br>and it is often large. The reliability of LSC or kriging using parameters with an error<br>of e.g. a quarter of the parameter value is usually not discussed.</p>}, number={1}, journal={Contributions to Geophysics and Geodesy}, author={JARMOŁOWSKI, Wojciech and BAKUŁA, Mieczysław}, year={2013}, month={Mar.}, pages={1-19} }