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

Conlet Biketi Kikechi,Richard Onyino Simwa

doi:10.5539/ijsp.v7n4p104

Abstract

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.

Highlights

The theory of sample surveys involves principles and methods of collecting and analyzing data from a finite population of N units and making inferences about finite population parameters on the basis of information obtained from the sample
The results of the bias and mean squared error (MSE) for the local polynomial regression estimator T0 for P = 0 and the local polynomial regression estimator T1 for P = 1 in the linear, quadratic and bump populations are provided in the table below
With regard to asymptotic relative efficiency, there is no difference in the performance of the local polynomial regression estimator T0 studied in this paper and the local polynomial regression estimator T1 studied by Kikechi et al (2018)

Summary

Introduction

The theory of sample surveys involves principles and methods of collecting and analyzing data from a finite population of N units and making inferences about finite population parameters on the basis of information obtained from the sample. An estimator of the finite population total is developed and its properties derived using the local polynomial regression procedure. Local polynomial regression is a nonparametric technique which is a generalization of kernel regression and is used for smoothing scatter plots and modeling functions. P is the order of the local polynomial being fit. A low order weighted least squares regression is fit at each point of interest x, using data from some neighborhood around x ( see Cleveland (1979) and Cleveland and Devlin (1988))

Methods

Discussion

Conclusion