Summary
We give several conditions on the estimator of efficient score function for estimating the parametric component of semiparametric models. A semiparametric version of the one-step MLE using an estimator of efficient score function which fulfills the conditions is shown to converge to the normal distribution with minimum variance locally uniformly over a fairly large neighborhood around the assumed semiparametric model. Consequently, it is shown to be asymptotically minimax with bounded subconvex loss functions. A few examples are also considered.
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Park, B.U. Asymptotic minimax estimation in semiparametric models. Probab. Th. Rel. Fields 88, 107–120 (1991). https://doi.org/10.1007/BF01193584
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DOI: https://doi.org/10.1007/BF01193584