On Differentials, Asymptotic Normality and Almost Sure Behavior of Statistical Functions, with Application to M-Statistics for Location Parameters.

Abstract

Parameters of interest in statistics can often be expressed as functionals T(F) of the underlying population distribution function, in which case a natural sample analogue estimator is provided by the statistical function T(F sub n) based upon the sample distribution function F sub N. Several notions of differentiability of functionals T are formulated, including innovations designed to broaden the scope of statistical application. Methodology for finding the differential, and for utilizing it to characterize the asymptotic distribution and almost sure behavior of statistical functions, is presented. Typically this means asymptotic normality and the law of the iterated logarithm.

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Document Details

Document Type
Technical Report
Publication Date
May 01, 1977
Accession Number
ADA042661

Entities

People

  • Dennis D. Boos
  • Robert Serfling

Organizations

  • Florida State University

Tags

Communities of Interest

  • C4I

DTIC Thesaurus Topics

  • Analogs
  • Asymptotic Normality
  • Continuity
  • Data Science
  • Distribution Functions
  • Equations
  • Estimators
  • Information Science
  • New York
  • Normality
  • Order Statistics
  • Probability
  • Random Variables
  • Statistical Algorithms
  • Statistical Functions
  • Statistics
  • Stochastic Processes

Fields of Study

  • Mathematics

Readers

  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)
  • Operations Research
  • Theoretical Analysis.