報 告 人：金百鎖 教授

報告題目：Spatial weights matrix selection and model averaging for spatial generalized linear model  

報告時間：2024年5月17日（周五）下午16:00

報告地點：靜遠樓1508學術(shù)報告廳

主辦單位：數(shù)學與統(tǒng)計學院、數(shù)學研究院、科學技術(shù)研究院

報告人簡介：

       金百鎖，中國科學技術(shù)大學管理學院統(tǒng)計與金融系教授。2001年畢業(yè)于中國科學技術(shù)大學獲得學士學位，2006年獲得中國科學技術(shù)大學博士學位。研究方向為變結(jié)構(gòu)模型，隨機矩陣，空間統(tǒng)計等。在PNAS，AoS，Biometrika，AAP等期刊已發(fā)表學術(shù)論文50余篇。主持承擔國家自然科學基金面上項目、重大項目課題、重點項目課題、國際交流項目等。現(xiàn)為中國現(xiàn)場統(tǒng)計研究會理事，中國現(xiàn)場統(tǒng)計研究會教育統(tǒng)計分會常務理事、秘書長，中國現(xiàn)場統(tǒng)計研究會旅游大數(shù)據(jù)分會常務理事、副理事長，中國現(xiàn)場統(tǒng)計研究會多元統(tǒng)計應用專業(yè)委員會 常務理事。

報告摘要：

       Spatial weights matrix selection and model averaging for spatial generalized linear model. For analyzing non-normal data that are observed from all the spatial units, we proposed a generalized linear model, whose link function has autoregressive construction for spatial interaction. In this article, we develop an approach that uses instrumental variables (IVs) to derive maximum likelihood estimators for the parameters. It is conceptually simple and easier to implement. Under mild conditions, it is shown that the estimator resulting from two-stage MLE is consistent and asymptotically normally distributed. Base on the proposed method, we employ the Kullback-Leibler (KL) loss function with a penalty term (Zhang et al.,2016) to choose the true spatial weights matrix or the best one in the sense of minimizing of KL loss. Additionally, we introduce a model averaging procedure to effectively reduce the KL loss. Extensive simulation studies and data examples demonstrate the effectiveness of the proposed method.