Theory & Methods: 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 n½. 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 L1 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.