On local polynomial regression estimators in finite populations

Abstract

This article examines the local polynomial regression estimators for the mean regression functions m _0 (x_j ) and m _1 (x_j ) in finite populations under circumstances when the order of the local polynomial being fit p is 0 and 1 respectively. The study utilizes a measure of performance that centres on the efficiency of the estimators of the mean regression function in survey sampling theory. To a greater extent, the examination considers analytical comparisons of the estimators in line with the concept of asymptotic relative efficiency. Particularly, asymptotic properties of the local constant regression estimator of the mean regression function are studied in a model based framework. The results of the local constant regression estimator of the mean regression function m _0 (x_j ) are compared with those of the local linear regression estimator of the mean regression function m _1 (x_j ) studied by Kikechi et al. (2017). Variance comparisons are made using the local constant regression estimator m _0 (x_j ) and the local linear regression estimator m _1 (x_j ) which show that the estimators are asymptotically equivalently efficient.