统计学系系列讲座之337期

时　间：2019年4月26日（星期五）10:00-11:00

地　点：史带楼301室

主持人：朱仲义教授 复旦大学管理学院统计学系

主　题：Estimation and Inference for Generalized Geoadditive Models

主讲人：杨立坚 教授　清华大学统计学研究中心

摘　要：

In many application areas, data are collected on a count or binary response with spatial covariate information. In this paper, we introduce a new class of generalized geoadditive models (GGAMs) for spatial data distributed over complex domains. Through a link function, the proposed GGAM assumes that the mean of the discrete response variable depends on additive univariate functions of explanatory variables and a bivariate function to adjust for the spatial effect. We propose a two-stage approach for estimating and making inferences of the components in the GGAM. In the first stage, the univariate components and the geographical component in the model are approximated via univariate polynomial splines and bivariate penalized splines over triangulation, respectively. In the second stage, local polynomial smoothing is applied to the cleaned univariate data to average out the variation of the first-stage estimators. We investigate the consistency of the proposed estimators and the asymptotic normality of the univariate components. We also establish the simultaneous confidence band for each of the univariate components. The performance of the proposed method is evaluated by two simulation studies. We apply the proposed method to analyze the crash counts data in the Tampa-St. Petersburg urbanized area in Florida.

Joint work with Shan Yu, Guannan Wang, Li Wang and Chenhui Liu

 统计学系 

2019-4-19