Nonsmooth Analysis and Frechet Differentiability of M-Functionals.

Abstract

A necessary requirement for existence of the Frechet derivative is that the defining psi function is uniformly bounded, and this naturally excludes those nonrobust estimators such as the maximum likelihood estimator in normal parametric models. In this paper the methods of nonsmooth analysis, described in the book by F.H. Clarke (1983), are introduced to the theory of statistical expansions, and are used here in the proofs of weak continuity and Frechet differentiability of M-functionals. Subsequently the conditions for Frechet differentiability given in Clarke (1983) can be relaxed to include most popular M-functionals. Additional keywords: distribution functions; M-estimators; robustness; gross error sensitivity; weak continuity; asymptotic expansions; asymptotic normality; selection functional; local uniqueness. (Author).

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Document Details

Document Type
Technical Report
Publication Date
Jun 01, 1984
Accession Number
ADA152932

Entities

People

  • B. R. Clarke

Organizations

  • University of North Carolina at Chapel Hill

Tags

DTIC Thesaurus Topics

  • Applied Mathematics
  • Asymptotic Normality
  • Asymptotic Series
  • Classification
  • Continuity
  • Data Science
  • Distribution Functions
  • Estimators
  • Information Science
  • Mathematics
  • Normality
  • Probability
  • Sensitivity
  • Sequences
  • Statistical Functions
  • Statistics
  • Universities

Fields of Study

  • Mathematics

Readers

  • Calculus or Mathematical Analysis
  • Statistical inference.