DENSITY ESTIMATION BY ORTHOGONAL SERIES.

Abstract

Given a random sample x sub 1...,x sub n from the density f(x) = Summation of (alpha sub m phi sub m(x)) where (braces) phi sub m(x) is an orthogonal basis, the estimator f star sub n(x) = Summation from zero to infinity of (lambda sub m(n) a sub m phi sub m(x)) where a sub m = (1/n) Summation from k = 1 to k = n, of phi sub m(x sub k) is suggested. f star sub n(x) will be a minimum integrated mean square error estimator in its class. These estimators are related to the kernel estimators discussed by Watson and Leadbetter (Ann. Math. Statist. 1963, 34, 480-491.).

Document Details

Document Type
Technical Report
Publication Date
Apr 01, 1968
Accession Number
AD0668155

Entities

People

  • Geoffrey S. Watson

Organizations

  • Johns Hopkins University

Tags

DTIC Thesaurus Topics

  • Algorithms
  • Computing-Related Activities
  • Data Science
  • Estimators
  • Information Science
  • Interdisciplinary Science
  • Mathematics
  • Statistical Algorithms
  • Statistical Analysis
  • Statistical Samples

Readers

  • Analytical Mechanics
  • Statistical inference.