A conditional perspective of weighted variance estimation of the optimal regression estimator |
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| Affiliation: | 1. Department of Computer, Control and Management Engineering Antonio Ruberti (DIAG), University of Rome “La Sapienza”, Via Ariosto 25, Rome 00185, Italy;2. Dipartimento di Ingegneria dell’Energia, dei Sistemi, del Territorio e delle costruzioni (DESTEC), University of Pisa, Italy and National Agency for the Evaluation of Universities and Research Institutes (ANVUR);3. ISBA, Université Catholique de Louvain, Louvain-la-Neuve, Belgium and DIAG University of Rome “La Sapienza”, Italy;1. Department of Economics, McGill University, Montréal, QC, Canada;2. Cornell University, Ithaca, NY, United States |
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| Abstract: | ![]()
The estimation of the variance for the GREG (general regression) estimator by weighted residuals is widely accepted as a method which yields estimators with good conditional properties. Since the optimal (regression) estimator shares the properties of GREG estimators which are used in the construction of weighted variance estimators, we introduce the weighting procedure also for estimating the variance of the optimal estimator. This method of variance estimation was originally presented in a seemingly ad hoc manner, and we shall discuss it from a conditional point of view and also look at an alternative way of utilizing the weights. Examples that stress conditional behaviour of estimators are then given for elementary sampling designs such as simple random sampling, stratified simple random sampling and Poisson sampling, where for the latter design we have conducted a small simulation study. |
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