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This article discusses the local polynomial regression estimator for  and the local polynomial regression estimator for  in a finite population. The performance criterion exploited in this study focuses on the efficiency of the finite population total estimators. Further, the discussion explores analytical comparisons between the two estimators with respect to asymptotic relative efficiency. In particular, asymptotic properties of the local polynomial regression estimator of finite population total for  are derived in a model based framework. The results of the local polynomial regression estimator for  are compared with those of the local polynomial regression estimator for  studied by Kikechi et al (2018). Variance comparisons are made using the local polynomial regression estimator  for  and the local polynomial regression estimator  for  which indicate that the estimators are asymptotically equivalently efficient. Simulation experiments carried out show that the local polynomial regression estimator  outperforms the local polynomial regression estimator  in the linear, quadratic and bump populations.

On Comparison of Local Polynomial Regression Estimators for P=0 and P=1 in a Model Based Framework