Abstract: Let (Y_𝒾 , θ_𝒾) , 𝒾 = 1 ,..., 𝓃 , be independent random vectors distributed as (Y , θ ) ~ G^* , where the marginal distribution of θ is completely unknown, and the conditional distribution of Y conditional on θ is known. It is desired to estimate G^* , as well as E_G* ℎ (Y , θ) for a given ℎ , based on the observed Y ₁ ,..., Y _n . In this paper we suggest a method for these problems and discuss some of its applications. The method involves a quadratic programming step. It is computationally efficient and may handle large data sets, where the popular method that uses EM-algorithm is impractical. The general approach of empirical Bayes, together with our computational method, is demonstrated and applied to problems of treating non-response. Our approach is nonstandard and does not involve missing at random type of assumptions. We present simulations, as well as an analysis of a data set from the Labor Force Survey in Israel. We also suggest a method, that involves convex optimization for constructing confidence intervals for E_G* ℎ under the above setup.

Key words and phrases: Non-Response, NPMLE.