Robust Model-Based and Model-Assisted Predictors of the Finite Population Total

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.

Download Full-text

Comparison of Various Methods for Estimating Finite Population Total in Survey Sampling When Study Variable and Auxiliary Variable are Inversely Related

Journal of Scientific Research ◽

10.3329/jsr.v11i1.36922 ◽

2019 ◽

Vol 11 (1) ◽

pp. 15-22

Author(s):

S. Kumar ◽

B. V. S. Sisodia

Keyword(s):

Simulation Study ◽

Finite Population ◽

Auxiliary Variable ◽

Survey Sampling ◽

The Other ◽

Regression Estimator ◽

Study Variable ◽

Population Total ◽

Model Based ◽

Proposed Model

In the present paper, a model based calibration estimator of population total has been developed when study variable y and auxiliary variable x are inversely related. The relative performance of the proposed model based calibration estimator in comparison to model based estimator, the usual regression estimator and calibration based regression estimator have been examined by conducting a limited simulation study. In view of the results of the simulation study, it has been found that model based calibration estimator has outperformed the other estimators. However, calibration based regression estimator was found to be close to the model based calibration estimator.

Download Full-text

Optimal prediction for a finite population total with connected designs and related model-based results

Metrika ◽

10.1007/bf01894730 ◽

1986 ◽

Vol 33 (1) ◽

pp. 79-84 ◽

Cited By ~ 3

Author(s):

R. Arnab

Keyword(s):

Finite Population ◽

Optimal Prediction ◽

Population Total ◽

Related Model ◽

Model Based

Download Full-text

A Boundary Corrected Non-Parametric Regression Estimator for Finite Population Total

International Journal of Statistics and Probability ◽

10.5539/ijsp.v8n3p83 ◽

2019 ◽

Vol 8 (3) ◽

pp. 83

Author(s):

Langat Reuben Cheruiyot ◽

Odhiambo Romanus Otieno ◽

George O. Orwa

Keyword(s):

Boundary Problem ◽

Nonparametric Regression ◽

Finite Population ◽

Simulated Data ◽

The Other ◽

Ratio Estimator ◽

Regression Estimator ◽

Population Total ◽

Parametric Regression ◽

Model Based

This study explores the estimation of finite population total. For many years design-based approach dominated the scene in statistical inference in sample surveys. The scenario has since changed with emergence of the other approaches (Model-Based, Model-Assisted and the Randomization-Assisted), which have proved to rival the conventional approach. This paper focuses on a model based approach. Within this framework a nonparametric regression estimator for finite population total is developed. The nonparametric technique has been found from previous studies to be advantageous than its parametric counterpart in terms of robustness and flexibility.  Kernel smoother has been used in construction of the estimator. The challenge of the boundary problem encountered with the Nadaraya-Watson estimator has been addressed by modifying it using reflection technique. The performance of the proposed estimator has been compared to the design-based Horvitz Thompson estimator and the model –based nonparametric regression estimator proposed by (Dorfman, 1992) and the ratio estimator using simulated data.

Download Full-text