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Statistics in natural sciences and technology Location: 0.001 Session Chair: Gaby Schneider Session Chair: Ansgar Steland | |
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The second order generalization of Hájek-Le Cam asymptotic minimax theorem Nanzan University, Japan The basic results concerning with the asymptotic theory of estimation and testing, Le Cam (1960) introduced so-called locally asymptotically normal (LAN) family of distributions. The convolution theorem for LAN case is obtained by Hájek (1970). The convolution result was extended by Le Cam (1972) to more general situations than that of LAN case. These results sometimes called the Hájek-Le Cam asymptotic minimax theorem. In this talk we derive the second order generalization of Hájek's convolution theorem. Furthermore, as a application of the second order Hájek's convolution theorem, we lead to the second order Hájek-Le Cam asymptotic minimax theorem. It automatically provides the conditions that the second order asymptotic efficient estimators should satisfy. | |
