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M-Estimation for Discrete Data: Asymptotic Distribution Theory and Implications.

Author: Douglas G Simpson; Raymond J Carroll; David Ruppert; NORTH CAROLINA UNIV AT CHAPEL HILL Dept. of STATISTICS.
Publisher: Ft. Belvoir Defense Technical Information Center NOV 1985.
Edition/Format:   Print book : EnglishView all editions and formats
Summary:
The asymptotic distribution of an M-estimator is studied when the underlying distribution is discrete. Asymptotic normality is shown to hold quite generally within the assumed parametric family. When the specification of the model is inexact, however, it is demonstrated that an M-estimator with a non-smooth score function, e.g. a Huber estimator, has a non-normal limiting distribution at certain distributions,  Read more...
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Document Type: Book
All Authors / Contributors: Douglas G Simpson; Raymond J Carroll; David Ruppert; NORTH CAROLINA UNIV AT CHAPEL HILL Dept. of STATISTICS.
OCLC Number: 227678458
Description: 23 pages

Abstract:

The asymptotic distribution of an M-estimator is studied when the underlying distribution is discrete. Asymptotic normality is shown to hold quite generally within the assumed parametric family. When the specification of the model is inexact, however, it is demonstrated that an M-estimator with a non-smooth score function, e.g. a Huber estimator, has a non-normal limiting distribution at certain distributions, resulting in unstable inference in the neighborhood of such distributions. Consequently, smooth score functions are proposed for discrete data. Keywords: Robust estimation; M estimator; Discrete parametric model; Smooth score function.

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