Efficient nonparametric estimation for skewed distributions

Many variables encountered in practice have skewed distributions. While the sample mean is unbiased for the true mean regardless of the underlying distribution that generated the sample observations, it can be highly unstable in the context of skewed distributions. To cope with this problem, we propose an efficient estimator of the population mean based on the concept of conditional bias of a unit, which can be viewed as a measure of its influence. The idea is to reduce the impact of the sample units that have a large influence. The resulting estimator depends on a cut-off value. We suggest selecting the cut-off value that minimizes the maximum absolute estimated conditional bias with respect to the proposed estimator. An estimator of the mean square error is also presented. An empirical investigation comparing several estimators in terms of relative bias and relative efficiency suggests that the proposed estimator and the estimator of its mean square error perform well for a wide class of distributions.

Automated summary

The article proposes an efficient estimator for the population mean based on the concept of conditional bias, aiming to reduce the impact of sample units with large influence in skewed distributions. It suggests selecting a cut-off value that minimizes the maximum absolute estimated conditional bias, and also presents an estimator for mean square error. Empirical investigation shows that the proposed estimator performs well for a wide class of distributions in terms of relative bias and efficiency.