Necessary and Sufficient Conditions for the Convergence of Integrated and Mean-Integrated r-th Order Error of Histogram Density Estimates.

Abstract

Suppose that X sub 1,...,X sub n are iid. samples drawn from a d-dimensional population with density function f. Let f(x) sub n = f sub n sub (x;X sub 1,....,X sub n) be an estimator of f(x). The Integrated Square Error (ISE) and Mean Integrated Square Error (MISE) of f sub n are important and widely used criteria in evaluating the performance of an estimator f sub n. Quite a lot of works appeared in the statistical literature dealing with the asymptotic properties of them, for various types of estimators, such as kernel estimator, orthogonal series estimator, nearest neighbor estimator etc. This paper the authors describe the necessary and sufficient conditions for the histogram estimator.

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Document Details

Document Type
Technical Report
Publication Date
Apr 01, 1987
Accession Number
ADA186037

Entities

People

  • L. C. Zhoa
  • X. R. Chen

Organizations

  • University of Pittsburgh

Tags

DTIC Thesaurus Topics

  • Air Force
  • Air Force Facilities
  • Classification
  • Consistency
  • Convergence
  • Data Science
  • Estimators
  • Governments
  • Histograms
  • Inequalities
  • Information Science
  • Multivariate Analysis
  • Probability
  • Probability Density Functions
  • Sequences
  • United States Government
  • Universities

Fields of Study

  • Mathematics

Readers

  • Statistical inference.