Local Polynomial Regression Estimator of the Finite Population Total under Stratified Random Sampling: A Model-Based Approach

Abstract

In this paper, auxiliary information is used to determine an estimator of finite population total using nonparametric regression under stratified random sampling. To achieve this, a model-based approach is adopted by making use of the local polynomial regression estimation to predict the nonsampled values of the survey variable y. The performance of the proposed estimator is investigated against some designbased and model-based regression estimators. The simulation experiments show that the resulting estimator exhibits good properties. Generally, good confidence intervals are seen for the nonparametric regression estimators, and use of the proposed estimator leads to relatively smaller values of RE compared to other estimators.

The Curve Estimation of Combined Truncated Spline and Fourier Series Estimators for Multiresponse Nonparametric Regression

“…The result in Equation (13) shows that curve estimation of the proposed model leads to the use of an error variance-covariance matrix as a weighting matrix. Hence, estimation of the error variance-covariance matrix is presented in Theorem 3.…”

“…To date, researchers have investigated various functions for estimating the regression curve in nonparametric regression, such as spline [3][4][5][6], Fourier series [7][8][9], kernel [10][11][12], polynomial [13][14][15], and wavelet [16][17][18] functions. The present study explores the nonparametric regression approach to analyzing spatial data, i.e., the use of the nonparametric truncated spline function in geographically weighted regression [19,20].…”