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A General Theory of Prediction in Finite Populations

1985; Wiley; Volume: 53; Issue: 3 Linguagem: Inglês

10.2307/1402888

1751-5823

Josemar Rodrigues, Heleno Bolfarine, André Rogatko, André Rogatko,

Survey Sampling and Estimation Techniques

Summary In this paper, we adopt the superpopulation approach to a finite population to develop a general theory of prediction for linear and quadratic functions of the population units. Most of the efforts are devoted to the problem of predicting quadratic forms, the population variance in particular, since much more attention has lately been devoted to the problem of the prediction of linear functions. As Godambe (1966), the problems considered are those for which the Gauss-Markov set-up of estimation is inapplicable. Several new predictors based on classical and Bayesian approaches to the population variance are formulated. The classical approach is based on the idea of totally sufficient statistics (Lauritzen, 1974). Some properties like unbiasedness, mean squared error and sensitivity to model misspecification of the derived predictors are studied. An attempt to characterize robustness conditions for protecting against model misspecification is formulated. An empirical investigation, based on a simulated population, is made to compare the performance of the suggested predictors.