| Summary: | 碩士 === 國立臺北大學 === 統計學系 === 96 === This paper aims to compare the estimators of regression coefficients under stratified sampling with unequal probability based upon a Monte Carlo approach. Recently, regression analysis has become popular with complex surveys. This paper intends to compare alternative estimators for regression coefficients under a complex survey. The alternative estimators used in this paper include least squares estimator, stratified weighted least squares estimator, probability weighted least squares estimator, and Quasi-Aitken weighted least squares estimator. Least squares methods which ignore population structure and sampling design could give seriously misleading results. There are two findings summarized from previous studies: (1) the least squares estimator is a common choice of researchers, but under an unequal probability design, the estimator is biased, (2) the probability weighted estimator is consistent but may have a large variance. Monte Carlo approach is used in this paper to compare the efficiency of the four estimators of regression coefficients based upon bias, variance, and MSE. The simulation results show that probability weighted least squares estimator and Quasi-Aitken weighted least squares estimator are unbiased estimators of regression coefficients. The simulation results also find that the Quasi-Aitken weighted least squares estimator has a smaller asymptotic variance than least squares estimator.
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