Convergence in distribution of the L2-deviations of the kernel-type variogram estimators with applications
| Autor: | Pilar García-Soidán, Tomás R. Cotos-Yáñez |
|---|---|
| Rok vydání: | 2017 |
| Předmět: |
Statistics and Probability
Mathematical optimization 0208 environmental biotechnology Kernel density estimation Estimator 02 engineering and technology Management Monitoring Policy and Law 01 natural sciences Least squares 020801 environmental engineering 010104 statistics & probability Convergence of random variables Goodness of fit Consistency (statistics) Kernel (statistics) Applied mathematics 0101 mathematics Computers in Earth Sciences Variogram Mathematics |
| Zdroj: | Spatial Statistics. 22:338-357 |
| ISSN: | 2211-6753 |
| DOI: | 10.1016/j.spasta.2017.02.002 |
| Popis: | In this work, some properties of the L 2 -deviations of the Nadaraya–Watson variogram estimators are analyzed, for both the anisotropic and the isotropic settings. Their convergence in distribution is established, which provides the basis for addressing practical problems, such as the construction of goodness of fit tests for the variogram and, therefore, for modeling the spatial dependence. However, the development of the latter application requires solving different issues, such as the approximation of the model parameters and the critical points. For estimation of the former ones, we propose proceeding through the least squares criteria, whose consistency will be proved, together with a reformulation of the global measures for the kernel-type estimators. Then, the resulting critical points can be approximated by appealing to the bootstrap approaches. Numerical studies with simulated and real data have been developed to illustrate the potentiality of our results, in order to check the appropriateness of a variogram model selected for the variogram. |
| Databáze: | OpenAIRE |
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