Simultaneous confidence intervals on partial means of classes in the two-stage stratified sampling |
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Authors: | Paolo C Cozzucoli |
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Institution: | (1) Department of Mathematics and Statistics, University of Canterbury, Private Bag 4800, Christchurch, New Zealand;(2) Department of Mathematical Sciences, Isfahan University of Technology, 84156-83111 Isfahan, Iran;(3) US Geological Survey, Leetown Science Centre, 11649 Leetown Rd, Kearneysville, WV 25430, USA |
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Abstract: | Let’s consider a finite population of P units, each of them assumes a specific amount of the quantitative variable X. Moreover we assume that the range of values of X is subdivided into k classes and the sampling data come out from a two stage stratified sampling. The main purpose of the work is to determine
the estimators, as well as their asymptotic distribution, of the partial means of classes, each of them is defined as a non
linear function of the other parameters. Particularly, we are interested in determining the linear approximation estimators
and, under convergence theorems, the asymptotic distribution. Afterwards we define the estimator of the vector of the partial
means of classes and its asymptotic convergence to multivariate normal distribution is determined. These results are useful
to develop simultaneous inferential procedures. |
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