Örnekleme Kuramında Yüzdelik Tahmin Edicileri

Abstract

Economic variables can have extreme values and in this case, these extreme values have a very strong impact on the mean. In such cases, using median and quantiles is more convenient instead of using mean. In literature, there have been many studies for estimating the population mean, population total and population variance but relatively less effort has been devoted to the development of efficient methods for estimating the population median and quantiles. In this study, quantile estimators, which are used in simple random sampling, successive sampling and two-phase sampling, are introduced. Mean squared error equations of these estimators are obtained and estimators are compared with each other in terms of mean squared errors. In addition, the calibration methods have been examined in the estimation of quantiles. New quantile estimators are proposed in simple random sampling and in stratified random sampling, mean squared error equations are obtained and the efficiencies of estimators are discussed. Asymptotic variance and mean squared error equations of classical, ratio and difference estimators, which are given in literature are compared with first proposed family of estimator of 𝑄������� ̂ Ö𝑖������� 1 in terms of mean squared errors. It is seen that the family of estimator of 𝑄������� ̂ Ö𝑖������� 1 is always more efficient than the classical, ratio and difference quantile estimators. Ratio and difference quantile estimators, including separate and combined estimates, are proposed in iv

stratified random sampling. In addition, the first proposed a family of estimator in simple random sampling is adapted to separate and combined estimates in the stratified random sampling. It is shown that, within the proposed estimators for separate and combined estimates in stratified random sampling, the proposed family of estimators are always more efficient than the classical, ratio and difference estimators. In the simple random sampling method, two different data sets are taken into account to compare the efficiencies of estimators. A numerical example is also given to compare efficiencies of the proposed estimators in stratified random sampling. In order to examine the efficiencies of the estimators in the literature, the mean squared error values of the estimators are calculated. The obtained results are interpreted.