On the estimation of the variance of the median used in L1linear inference procedures

Abstract

Recent results in the literature have considered the distri-bution of the LAV estimator ; i.e, under the criterion of min-izing the sum of absolute deviations. It has been shown that is approximately normally distributed with mean zero and covarianoe matrix where λ²/n is the variance of the median for a sample of size n. Sub-sequent research has shown how the asymptotic results can be used in inference procedures; these procedures are based on λ being known. This paper will consider the estimation of λ as suggested by Cox and Hinkley (1974). In this spirit a Monte Carlo study was conducted using various distributions over various sample sizes. Guidelines for using this estimate of λ in LAV inference proce-dures will also be discussed.