Statistical Inference And Influence Analysis Of Geographically And Temporally Weighted Regression Model

With the expanding range of statistical applications, people have paid more andmore attention to the statistical analysis of spatio-temporal data. In regard to thelarge spatio-temporal data whose production mechanism is complicated, it is unrealis-tic to assume that the structure of the data is homogeneity to research the relationshipbetween a variable and other variables in the data set. Geographically and tempo-rally weighted regression model is the promotion of geographically weighted regressionmodel. Geographically and temporally weighted regression model assume that the re-gression coefcients are the functions of geographical location and observation time invarying-coefcient models. Spatial and temporal characteristics of data are involvedin geographically and temporally weighted regression model, which set the stage forexploring the spatial nonstationarity and temporal nonstationarity of the regressionrelation. The ftting method、statistical inference and infuence analysis of geograph-ically and temporally weighted regression model have been researched in this article.The ftting method of geographically and temporally weighted regression modelis given based on the theory of weighted least squares estimate, the related selectprinciple of weight function and cross-validation for fxing bandwidth parameter arealso provided. The statistical properties of the estimator and the ftted values of thedependent variable are researched from the point of mathematical expectation andvariance.For hypothesis testing of global stationarity、spatial nonstationarity and tem-poral nonstationarity, making use of the idea of variance analysis, the test statisticsare given respectively based on the residual sum of squares. There is an importantassumption that the variances of the error terms are equal in observation area in theftting method of geographically and temporally weighted regression model. However,this assumption is not justifed in many practical observations. Based on this consid-eration, the Score test statistic of heteroscedasticity signifcant test of error is givenin geographically and temporally weighted regression model.In addition, we hope to gain the stable empirical regression equation in statisticalanalysis. However, when the data set are applied to estimate the model parameters,if some data points of the data set have abnormal efect on parameter estimationor away from the main body of data set, the ftting results of model will be poor.Based on this consideration, the ftting infuence degree of each observational data is discussed upon the data deletion model and the Cook statistic is given. The problemof outlier test is researched and the test statistic is given.