Font Size: a A A

Statistical Inference Of The Spatial Matérn Covariance Model And Spatial Logistic Model

Posted on:2021-10-02Degree:DoctorType:Dissertation
Country:ChinaCandidate:Y P HongFull Text:PDF
GTID:1487306542496254Subject:Statistics
Abstract/Summary:PDF Full Text Request
In this dissertation,we consider some problems on the spatial inference of the spatial Matérn covariance model and the spatial logistic covariance model.For the estimation of the smoothness parameter of the Matérn covariance model,determining a range of the smoothness parameter can help improve the result of this estimation.Therefore,we propose the one-tailed test and the chain-like testing procedure,which can determine an interval containing the true parameter from several candidates.The nice properties of the procedure are shown by the asymptotic results of the test statistic and the simulations.We also show the applications of the proposed procedure by selecting the tuning parameters in a local Whittle-like type estimator proposed by Wu et al.For prediction efficiency assessment of the Matérn covariance model,we propose the Mean Loss of Efficiency(MLOE)and Mean Misspecification of the Mean Square Error(MMOM)criteria to assess the spatial prediction performance.Compared with the common Mean Square Prediction Error criterion,our criteria can give more informative information for the loss of the prediction efficiency.To show the applications of these criteria,we compare the prediction efficiency of the Tile Low-Rank(TLR)approximation method proposed by Abdulah et al.with different tuning parameters by simulations and provide two kinds of suggestions for the tuning parameter settings.We also fit a dataset of soil moisture in the area of the Mississippi River basin,showing that our suggestions are reasonable,and the TLR method behaves better than the popular Gaussian predictive process method for this dataset.For the generalization of the autocovariance parameter in the spatial logistic model,we establish the spatial logistic model with spatial heterogeneity by introducing covariates in the autocovariance parameter.This model is suitable for the spatial dataset with bivariate responses,where the spatial distribution pattern varies with spatial locations.We give the Maximum Pseudo-Likelihood(MPL)estimator and introduce AIC and BIC criteria for model selection.Simulations show that the MPL estimator behaves well for most of the cases,and the BIC criterion is more suitable for model selection.
Keywords/Search Tags:Matérn covariance model, Chain-like testing procedure, Prediction efficiency, Spatial logistic model, Autocovariance parameter
PDF Full Text Request
Related items