Some new reflection principles for Maxwell's equations are first established, which are then applied to derive two novel identifiability results in inverse electromagnetic obstacle scattering problems with polyhed...Some new reflection principles for Maxwell's equations are first established, which are then applied to derive two novel identifiability results in inverse electromagnetic obstacle scattering problems with polyhedral scatterers.展开更多
It is well known that for one-dimensional normal EV regression model X=x+u,Y=α+βx+e,where x,u,e are mutually independent normal variables and Eu=Ee=0,the regression parameters a andβare not identifiable without som...It is well known that for one-dimensional normal EV regression model X=x+u,Y=α+βx+e,where x,u,e are mutually independent normal variables and Eu=Ee=0,the regression parameters a andβare not identifiable without some restriction imposed on the parameters.This paper discusses the problem of existence of unbiased estimate for a andβunder some restrictions commonly used in practice.It is proved that the unbiased estimate does not exist under many such restrictions.We also point out one important case in which the unbiased estimates of a andβexist,and the form of the MVUE of a andβare also given.展开更多
基金supported by NSF grant,FRG DMS 0554571supported substantially by Hong Kong RGC grant (Project 404407)partially by Cheung Kong Scholars Programme through Wuhan University,China.
文摘Some new reflection principles for Maxwell's equations are first established, which are then applied to derive two novel identifiability results in inverse electromagnetic obstacle scattering problems with polyhedral scatterers.
基金This work was supported by the National Natural Science Foundation of China(Grant No.10231030).
文摘It is well known that for one-dimensional normal EV regression model X=x+u,Y=α+βx+e,where x,u,e are mutually independent normal variables and Eu=Ee=0,the regression parameters a andβare not identifiable without some restriction imposed on the parameters.This paper discusses the problem of existence of unbiased estimate for a andβunder some restrictions commonly used in practice.It is proved that the unbiased estimate does not exist under many such restrictions.We also point out one important case in which the unbiased estimates of a andβexist,and the form of the MVUE of a andβare also given.
