Along the line of the classical generalized linear model, the classical generalized linear model is improved in this article by assuming the partial coefficients of the regressors to be arbitrary functions of the points in some metric space. This new type of regression model is called in this article semiparametric vary-coefficient generalized linear model and the back-fitting approach is suggested to fit the proposed model, and the smoothing parameter therein are studied. The proposed model not only have higher flexibility and adaptability, but also is suitable for analysis spatial data and therefore has extensive application backgrounds.
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