Matias Salibian-Barrera (Carleton University) Ruben H. Zamar (University of British Columbia)
Abstract
Most asymptotic results for robust estimates rely on regularity conditions that are difficult to verify and that real data sets rarely satisfy. Moreover, these results apply to fixed distribution functions. In the robustness context the distribution of the data remains largely unspecified and hence results that hold uniformly over a set of possible distribution functions are of theoretical and practical interest. In this paper we study the problem of obtaining verifiable and realistic conditions that suffice to obtain uniform consistency and uniform asymptotic normality for location robust estimates when the scale of the errors is unknown. We study M-location estimates calculated withan S-scale and we obtain uniform asymptotic results over contamination neighbourhoods. There is a trade-off between the size of these neighbourhoods and the breakdown point of the scale estimate. We also show how to calculate the maximum size of the contamination neighbourhoods where these uniform results hold.
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Paper provided by Département des sciences administratives, UQO in its series RePAd Working Paper Series with number
lrsp-TRS375.
Length: 26 pages Date of creation: 10 Jun 2002 Date of revision: Handle: RePEc:pqs:wpaper:0122005
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Find related papers by JEL classification: C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - General C40 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - General