Approximate Variance of Least Square Estimators for Regression Coefficient under Inclusion Probability Proportional to Size Sampling

- Journal title : Communications for Statistical Applications and Methods
- Volume 19, Issue 1, 2012, pp.23-32
- Publisher : The Korean Statistical Society
- DOI : 10.5351/CKSS.2012.19.1.023

Title & Authors

Approximate Variance of Least Square Estimators for Regression Coefficient under Inclusion Probability Proportional to Size Sampling

Kim, Kyu-Seong;

Kim, Kyu-Seong;

Abstract

This paper deals with the bias and variance of regression coefficient estimators in a finite population. We derive approximate formulas for the bias, variance and mean square error of two estimators when we select a fixed-size inclusion probability proportional to the size sample and then estimate regression coefficients by the ordinary least square estimator as well as the weighted least square estimator based on the selected sample data. Necessary and sufficient conditions for the comparison of the two estimators in terms of variance and mean square error are suggested. In addition, a simple example is introduced to numerically compare the variance and mean square error of the two estimators.

Keywords

Approximate bias;approximate variance;inclusion probability proportional to size sampling;ordinary least square estimator;weighted least square estimator;

Language

Korean

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