EFFICIENT ESTIMATION USING BOTH DIRECT AND INDIRECT OBSERVATIONS

The Ibragimov-Khas'minskii model postulates observing X1,...,X(m) independent, identically distributed according to an unknown distribution G and Y1,...,Y(n) independent and identically distributed according to integral k(., y) dG(y), -here 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, infinity], k(x, y) = y-1 1 (x less-than-or-equal-to y).