Durağan Olmayan Uzamsal Kovaryans Yapılar İçin Uyarlanabilir Modeller

Abstract

Objective: In modeling environment processes, multi- disciplinary methods are used to explain, explore and predict how the earth responds to natural human-induced environmental changes over time. Consequently, when analyzing spatial processes spatial domains, the spatial covariance of interest are always heterogeneous. However, this article proposed locally adaptive covariance for the spatial domain whose covariance is nonstationary in their spatial domain. The objectives of the study are to propose parametric, non-parametric and semi- parametric models for nonstationary spatial structure, continuous model for nonstationary spatial processes whose distance is far apart and to propose the adaptive weighting scheme approach that generates the optimal value for the nonparametric and semi-parametric models. Material and Methods: The spatial covariances are derived by applying the concept of adaptive weighting scheme approach on the covariance proposed in Nott and Dunsmuir (2002). Consequently, the local adaptive bandwidth for the nonstationary covariance was obtained for both the nonparametric and semi-parametric models. Simulations are conducted on the proposed model to examine the proposed model. Results and Conclusion: The results obtained are compared with existing models. The results indicate proposed spatial covariance are driven by the local bandwidths, penalty, weighted scheme, and tuning parameters. The adaptive models performed better in relation to existing covariances in terms of their mean square prediction errors (MSPE). The proposed models were further applied to real life Sulphate spatial data.