Nonparametric Estimates of the Asymptotic Covariance Matrix Associated with BICKEL's Estimate for Multivariate Shift Parameters

Nonparametric estimates are proposed for the asymptotic covariance matrix associated with the vector of medians of averages of pairs when estimating the shift parameter in the multivariate one sample problem. These estimates are based on density estimation and are competitors to the “natural” estimate proposed by BICKEL (1965). Weak and strong consistency of the estimates as well as asymptotic normality are presented.