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

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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Document Details

Document Type
Technical Report
Publication Date
Nov 01, 1985
Accession Number
ADA168532

Entities

People

  • David Ruppert
  • Douglas G. Simpson
  • Raymond J. Carroll

Organizations

  • University of North Carolina at Chapel Hill

Tags

Communities of Interest

  • C4I

DTIC Thesaurus Topics

  • Classification
  • Data Science
  • Distribution Functions
  • Distribution Theory
  • Estimators
  • Information Science
  • New York
  • Normal Distribution
  • North Carolina
  • Optimal Estimators
  • Probability
  • Security
  • Standards
  • Statistical Algorithms
  • Statistical Analysis
  • Statistics
  • Universities

Fields of Study

  • Mathematics

Readers

  • Statistical inference.

Technology Areas

  • AI & ML
  • AI & ML - Bayesian Inference
  • AI & ML - Machine Learning Algorithms