Optimal Robust Estimation Based on Statistical Depth for Discrete Stochastic Processes

摘要

This paper gives a general method of constructing robust quasi-likelihood estimating functions via statistical depth for stationary processes. The obtained estimating functions and parameter estimation have desirable robustness, which attain very high breakdown values close to 1/(2(p+1)).At the same time, the obtained parameter estimation still has ordinary asymptotic behaviors such as asymptotic normality. An example of AR(1) model is presented to illustrate the methodology. We also discuss the change of efficiency involved in robustness.