Robust and Asymptotically Efficient Estimation of Location in a Stationary Strong Mixing Gaussian Parametric Model

This paper considers the problem of robust estimation of location in a model with stationary strong mixing Gaussian parametric distributions. An estimator is found that is within epsilon of being asymptotically efficient at the Gaussian parametric distribution and is within epsilon of being optimally robust! For the robustness results a Huber-type minimax criterion is used, where minimaxing takes place over neighborhoods of the parametric Gaussian distributions. The neighborhood system considered includes distributions of strong mixing processes and allows for deviations from the normal univariate parametric distributions within a Hellinger metric neighborhood, as well as deviations from stationarity and from the Gaussian structure of independence.