Median estimation using auxiliary variables

In the present study the estimation of the median has been taken into consideration using different methods of analysis. First of all the estimation of the median without auxiliary information is analyzed. Then the method of Kuk and Mak proposed in 1989 is exposed: this way of estimating the median is based on the knowledge of the population median of auxiliary variable X. Another method, which considers the median of the auxiliary variable is the ratio estimator. Then two methods based on the regression estimator are analyzed : the first one considers the regression based on the median regression, the second one is based on the minimum square method. Two experiments have been carried out in order to compare the methods proposed. First of all the methods are compared selecting all possible samples from nine di_erent small populations. The second application is based on the selection of couples of random numbers from a bivariate random variable distributed as a Bivariate Log-Normal distribution. Also in this situation the methods of estimation of the median are compared considering the expected values and mean square errors.