Median Estimation in Sample Surveys

In a recent paper Maritz and Jarrett (1978) proposed a small-sample estimate of the variance of sample medians from continuous population. In this paper their methods are adapted to median estimation in s~atified sampling without replacement from finite populations. A weighted sample median for estimating the median of heavy-tailed or skewed populations is proposed. Its asymptotic normal distribution is derived, and optimal allocation is discussed. A systematic statistic based on the ordered observations in the complete sample, for the estimation of the variance of the weighted median is proposed. This variance estimate is shown to be a consistent estimate of the weighted median asymptotic variance. Initial simulation results suggest a trimmed version of this estimate to be an efficient and computationally feasible alternative. Some results are also obtained for stratified sampling of clusters. The weighted median, based on the pooled clusters in each atratum, is shown to be a consistent and asymptotically normal estimate of the population median. A "Bookstrap" estimate of the variance of this estimate is proposed.