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Highly efficient weighted for autoregression wilcoxon estimes for autoregression 

Authors: Jeffrey T. Terpstra a;  Joseph W. McKean a; Joshua D. Naranjo b
Affiliations:   a North Dakota State University, USA
b Western Michigan University, USA
DOI: 10.1080/02331880108802724
Publication Frequency: 6 issues per year
Published in: journal Statistics, Volume 35, Issue 1 2000 , pages 45 - 80
Formats available: PDF (English)
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Abstract

In this paper we explore the use of Schweppe-type weights for a class of weighted Wiicoxon estimates and apply the corresponding estimates to an autoregressive time series model This special class of estimates is essentially the autoregressive analog of the HBR-estimates proposed by Chang et al. (1999) in the linear regression context. Assuming a stationary finite second moment autoregressive model of order p, asymptotic linearity properties are derived for the HBR-estimate. Based on these properties, the HBR-estimate is shown to be asymptotically normal at rate nl/2. Tests of general linear hypotheses as well as standard errors for confidence interval procedures can be based on such results. In a linear regression setting, the HBR-estimate is highly efficient and inherits a totally bounded influence function and a 50percent breakdown point. Examples and a Monte Carlo study over innovated and additive outlier models indicate that these properties of the HBR-estimate are preserved in an autoregressive time series context, Thus, the HBR-estimate provides a highly efficient and robust alternative for autoregressive time series estimation.
Keywords: Additive outliers; Autoregressive time series; Innovation outliers; High-breakdown estimates; Rank-based estimates; Schweppe weights; Wiicoxon estimates
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