Prediction of finite population parameters using parametric model under some loss functions

The fundamental problem in finite population sampling lies in the prediction of a function of the unobserved data based on the observed data. The original focus on the prediction of the finite population quantities has been supplemented recently by the use of statistical models. To this end, this paper uses a model-based inference and applies the Bayesian, robust Bayesian and frequentist approaches. Several robust Bayesian analysis criteria can be used for this purpose including the posterior regret gamma-minimax (PRGM), conditional gamma-minimax (CGM), and the most stable (MS). The aim of this paper is a comparison of the Bayesian, robust Bayesian and frequentist predictors of a general linear combination of the finite population values under a superpopulation model, which seems to apply in many practical problems, and several loss functions. Finally, a real-life example is provided to predict a finite population mean and compare the estimated risk and bias of the obtained predictors under the squared error (SE), linear-exponential (LINEX) and reflected normal (RN) loss functions by a simulation study.