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- W3125532033 abstract "We establish asymptotic normality and consistency for rank-based estima- tors of autoregressive-moving average model parameters. The estimators are obtained by minimizing a rank-based residual dispersion function similar to the one given by L.A. Jaeckel (Ann. Math. Stat. Vol. 43 (1972) 1449-1458). These estimators can have the same asymptotic efficiency as maximum likelihood estimators and are robust. The quality of the asymptotic approximations for finite samples is studied via simulation. In this article, we use a rank-based technique to estimate the parameters of autoregressive-moving average (ARMA) models, the standard linear time series models for stationary data. The rank (R) estimators we consider minimize the sum of mean-corrected model residuals weighted by a function of residual rank; they are similar to the R-estimators proposed by Jaeckel (1972) for estimating linear regression parameters. As discussed in Jureckovaand Sen (1996), R-estimators are, in general, robust and relatively efficient. We show this is true in the case of ARMA parameter estimation. The estimation technique is robust because the R-estimators of ARMA model parameters are consistent and asymptotically normal under very mild conditions on the noise distribution. Since the weight function can be chosen so that R-estimation has the same asymptotic efficiency as maximum likelihood (ML) estimation, the R-estimators are also relatively efficient. The relative efficiency of the estimators extends to the unknown noise distribution case since R-estimation with the Wilcoxon weight function (a linear weight function) is nearly as efficient as ML for a large class of noise distributions. In addition, R-estimation compares favourably with classical Gaussian quasi-ML estimation and least absolute deviations (LAD) estimation. We show that R-estimation with the van der Waerden weight function (the inverse of the standard normal distribution function) uniformly dominates Gaussian quasi-ML with respect to asymptotic efficiency, and we give a weight function for which R-estimation is asymptotically equivalent to LAD estimation." @default.
- W3125532033 created "2021-02-01" @default.
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- W3125532033 date "2007-01-01" @default.
- W3125532033 modified "2023-09-26" @default.
- W3125532033 title "RANK-BASED ESTIMATION FOR AUTOREGRESSIVE MOVING AVERAGE TIME SERIES MODELS" @default.
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