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Semiparametric and nonparametric calibration estimators in cluster sampling by use of penalty functions

Author Affiliations

  • 1Department of Statistics and Actuarial Sciences, Technical University of Kenya, P.O. BOX 52428-00200 Nairobi, Kenya

Res. J. Mathematical & Statistical Sci., Volume 6, Issue (4), Pages 1-10, April,12 (2018)

Abstract

The application of nonparametric model calibration estimators in multistage survey sampling has been studied by several authors with the cluster level auxiliary information assumed completely available for each cluster. The reasoning behind model calibration is that if the calibration constraints are satisfied by the auxiliary variable, then it is expected that the fitted values of the variable of interest should satisfy such constraints too. In this paper, we have considered a case of auxiliary information present at two levels. We derive estimators by treating the calibration problems at both levels as optimization problems and solving them by the method of penalty functions. We have shown that the estimators obtained are robust since they do not fail in the event the model is misspecified for the data.

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