Asymptotically Efficient Estimation of Linear Functionals in Inverse Regression Models
نویسندگان
چکیده
In this paper we will discuss a procedure to improve the usual estimator of a linear functional of the unknown regression function in inverse nonparametric regression models. In Klaassen et al. (2001) it has been proved that this traditional estimator is not asymptotically efficient (in the sense of the Hájek Le Cam convolution theorem) except, possibly, when the error distribution is normal. Since this estimator, however, is still root-n consistent a procedure in Bickel et al. (1993) applies to construct a modification which is asymptotically efficient. A self-contained proof of the asymptotic efficiency is included.
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