A Variation on Scheffe's Theorem, with Application to Nonparametric Density Estimation.

Abstract

For probability density functions (f sub n) and f defined on a d-dimensional Euclidean space, Scheffe proved the useful result that pointwise convergence of f sub n to f implies convergence in the mean as well. In some applications it is of interest to know the rate of the mean convergence, and, in particular, to connect it with the rate of the uniform pointwise convergence. A basic lemma of this type is derived and applied to some problems in nonparametric density estimation. (Author)

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Document Details

Document Type
Technical Report
Publication Date
May 01, 1979
Accession Number
ADA072132

Entities

People

  • Robert Serfling

Organizations

  • Florida State University

Tags

Communities of Interest

  • Autonomy

DTIC Thesaurus Topics

  • Abstracts
  • Analogs
  • Convergence
  • Data Science
  • Estimators
  • Inequalities
  • Information Science
  • Measure Theory
  • Military Research
  • Probability
  • Probability Density Functions
  • Probability Distributions
  • Sequences
  • Statistics
  • Theorems

Fields of Study

  • Mathematics

Readers

  • Mathematical Modeling and Probability Theory.
  • Regression Analysis.

Technology Areas

  • Space