ARTICLE
ABSTRACT
In this paper the case of a conditional sampling design proportional to the sum of two order statistics is considered. Several strategies including the Horvitz-Thompson estimator and ratio-type estimators are discussed. The accuracy of these estimators is analyzed on the basis of computer simulation experiments.
KEYWORDS
sampling design, order statistic, sample quantile, auxiliary variable, Horvitz-Thompson statistic, inclusion probabilities, sampling scheme, ratio estimator.
REFERENCES
HORVITZ, D., G., THOMPSON D. J., (1952). A generalization of the sampling without replacement from finite universe. Journal of the American Statistical Association, Vol. 47, 663–685.
LAHIRI G. W., (1951). A method for sample selection providing unbiased ratio estimator. Bulletin of the International Statistical Institute, Vol. 33,pp. 133–140.
MIDZUNO H., (1952). On the sampling system with probability proportional to the sum of sizes. Annals of the Institute of Statistical Mathematics, Vol. 3, pp. 99–107.
SA¨RNDAL C. E., SWENSSON B., WRETMAN J., (1992). Model Assisted Survey Sampling. Springer Verlag, New York-Berlin-Heidelberg-London Paris-Tokyo-Hong Kong-Barcelona-Budapest.
SEN A. R., (1953). On the estimate of variance in sampling with varying probabilities Journal of the Indian Society of Agicultural Statistics, 5, 2, pp. 119–127.
TILLE´ Y., (1999). Estimation in Surveys Using Conditional Inclusion Probabilities: Complex Design. Survey Methodology, Vol. 25, No 1, pp. 57–66.
TILLE´ Y., (2006). Sampling algorithms. Springer.
WYWIAŁ, J. L., (2007). Simulation analysis of accuracy estimation of population mean on the basis of strategy dependent on sampling design proportionate to the order statistic of an auxiliary variable. Statistics in Transition-new series,Vol. 8, No. 1, pp. 125–137.
WYWIAŁ, J. L., (2008). Sampling design proportional to order statistic of auxiliary variable. Statistical Papers, Vol. 49, No. 2, pp. 277–289.
WYWIAŁ, J. L., (2009). Performing quantiles in regression sampling strategy. Model Assisted Statistics and Applications, Vol. 4, No. 2, pp. 131–142
