Weighted Wilcoxon Estimates for Autoregression

This paper explores the class of weighted Wilcoxon (WW) estimates in the context of autoregressive parameter estimation, giving special attention to three sub-classes of so-called WW-estimates. When the weights are constant, the estimate is equivalent to using Jaeckel's estimate with Wilcoxon scores. The paper presents asymptotic linearity properties for the three sub-classes of WW-estimates. These properties imply that the estimates are asymptotically normal at rate n ^½. Tests of hypotheses as well as standard errors for confidence interval procedures can be based on such results. Furthermore, the estimates can be computed with an L ₁ regression routine once the weights have been calculated. Examples and a Monte Carlo study over innovation and additive outlier models suggest that WW-estimates can be both robust and highly efficient.