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Asymptotic linearity of minimax estimators
Author(s) -
Vaart A.W.
Publication year - 1992
Publication title -
statistica neerlandica
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.52
H-Index - 39
eISSN - 1467-9574
pISSN - 0039-0402
DOI - 10.1111/j.1467-9574.1992.tb01336.x
Subject(s) - mathematics , minimax , estimator , linearity , simple (philosophy) , statement (logic) , minimax estimator , parametric statistics , calculus (dental) , mathematical optimization , statistics , minimum variance unbiased estimator , medicine , philosophy , physics , dentistry , epistemology , quantum mechanics , political science , law
The celebrated local asymptotic minimax (LAM) theorem due to HÁjek (1972) also includes the statement that a LAM estimator Is necessarily asymptotically linear. A similar result. is true for semi‐parametric models, but Hájek's result doesn't apply to this case as the efficient influence function is often not contained in the (proper) tangent space. This note gives a simple, elementary proof of both the LAM theorem and the necessity of asymptotic linearity of a LAM estimator sequence.