Model-based estimation for population total under model misspecification using the balanced sampling scheme

Abstract

A common assumption in the model-based inference is that the model which explains the behavior of the random phenomena being investigated is correctly specified. But if model is incorrect, it turns out that the inference can be affected and the predictions can be poor, which leads to increase the bias of an estimator. In this article, a balanced sampling technique is introduced for reducing the model misspecification bias in estimating the finite population total where working model is deviates from the underlying true model. Some special cases like homogeneous population model, linear population model and ratio population model are considered under the misspecified basis function regression model by utilizing the model relationship. Design-based efficiency comparisons of the proposed estimators to the existing ones are evaluated through simulation and a real data set. It is shown that the proposed estimators using the balancing scheme keep up the superiority in simple random sampling.

KEYWORD:

• Misspecified model
• Model-based approach
• Non-informative sampling
• Simple random sampling
• Superpopulation model

Acknowledgments

The authors are very grateful to the editor and a reviewer for their careful reading of the paper and valuable comments which leads to a significant improvement in a manuscript.