Abstract #300591

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JSM 2002 Abstract #300591
Activity Number: 44
Type: Contributed
Date/Time: Sunday, August 11, 2002 : 4:00 PM to 5:50 PM
Sponsor: Section on Nonparametric Statistics*
Abstract - #300591
Title: Computing the Efficiency and Turning Constants for M-estimation
Author(s): Colin Chen*+ and Guosheng Yin
Affiliation(s): SAS Institute Inc. and University of North Carolina
Address: SAS Campus Drive , Cary, North Carolina, 27513,
Keywords: M-estimation ; asymptotic efficiency ; turning constant ; weight function
Abstract:

For the redescending M-estimation, the turning constant in the redescending $\psi$-function and the asymptotic efficiency of the M-estimator have a one-to-one relation. The computing of the asymptotic efficiency as a function of the turning constant, as well as the turning constant as a function of the asymptotic efficiency with a group of $\rho$-functions are discussed. While the asymptotic efficiency as a function of the turning constant can be computed by some closed forms with integrations, the reverse function does not have a closed form. We use some cumulative distribution functions to fit the turning constant with high accuracy.

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Revised March 2002