ON THE ESTIMATION OF THE PROBABILITY DENSITY

Abstract

Estimators of the form fn(x) = 1-n ni=1 n(x-xi), of a probability density f(x) are considered, where x1,...., xn is a sample of n observations from f(x). The properties of such estimators are discussed on the basis of their mean integrated square errors, E (fn(x) - f(x))2dx (M.I.S.E.), and also on the basis of various pointwise consistency criteria. The corresponding development for discrete distributions is sketched and examples are given in both continuous and discrete cases. The definitions and results are analogous to those of Parzen for the spectral density. (Author)

Document Details

Document Type
Technical Report
Publication Date
Sep 02, 1961
Accession Number
AD0264811

Entities

People

  • G.s. Watson
  • M.r. Leadbetter

Organizations

  • RTI International

Tags

DTIC Thesaurus Topics

  • Acquisition
  • Consistency
  • Discrete Distribution
  • Estimators
  • Mathematics
  • Observation
  • Probability

Fields of Study

  • Mathematics

Readers

  • Analytical Mechanics
  • Statistical inference.