Two-stage informative cluster sampling—estimation and prediction with applications for small-area models |
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Authors: | Abdulhakeem Eideh Gad Nathan |
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Institution: | 1. Department of Mathematics, Faculty of Science and Technology, Al-Quds University, Abu-Dies Campus, P.O. Box 20002, East Jerusalem, Palestine;2. Department of Statistics, Hebrew University of Jerusalem, Israel |
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Abstract: | This paper considers the effects of informative two-stage cluster sampling on estimation and prediction. The aims of this article are twofold: first to estimate the parameters of the superpopulation model for two-stage cluster sampling from a finite population, when the sampling design for both stages is informative, using maximum likelihood estimation methods based on the sample-likelihood function; secondly to predict the finite population total and to predict the cluster-specific effects and the cluster totals for clusters in the sample and for clusters not in the sample. To achieve this we derive the sample and sample-complement distributions and the moments of the first and second stage measurements. Also we derive the conditional sample and conditional sample-complement distributions and the moments of the cluster-specific effects given the cluster measurements. It should be noted that classical design-based inference that consists of weighting the sample observations by the inverse of sample selection probabilities cannot be applied for the prediction of the cluster-specific effects for clusters not in the sample. Also we give an alternative justification of the Royall 1976. The linear least squares prediction approach to two-stage sampling. Journal of the American Statistical Association 71, 657–664] predictor of the finite population total under two-stage cluster population. Furthermore, small-area models are studied under informative sampling. |
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Keywords: | Empirical best linear unbiased predictor Informative sampling Maximum likelihood estimation Pseudo-maximum likelihood Sample-likelihood function Small-area estimation |
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