Efficient estimation using both direct and indirect observations
نویسندگان
چکیده
The Ibragimov Hasminskii model postulates observing X1, . . . , Xm independent, identically distributed according to an unknown distribution G and Y1, . . . , Yn independent and identically distributed according to ∫ k(·, y)dG(y) where k is known, for example, Y is obtained from X by convolution with a Gaussian density. We exhibit sieve type estimates of G which are efficient under minimal conditions which include those of Vardi and Zhang (1992) for the special case, G on [0,∞], k(x, y) = 1 y 1(x ≤ y). Research supported by NSF Grant DMS-9115577 and the U.S./Israel Binational Science Foundation
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