On the Estimation of a Probability Density Function by the Maximum Penalized Likelihood Method.

Abstract

A class of probability density estimates can be obtained by penalizing the likelihood by a functional which depends on the roughness of the logarithm of the density. The limiting case of the estimates as the amount of smoothing increasing has a natural form which makes the method attractive for data analysis and which provides a rationale for a particular choice of roughness penalty. The estimates are shown to be the solution of an unconstrained convex optimization problem, and mild natural conditions are given for them to exist. Rates of consistency in various norms and conditions for asymptotic normality and approximation by a Gaussian process are given, thus breaking new ground in the theory of maximum penalized likelihood density estimation. (Author)

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Document Details

Document Type
Technical Report
Publication Date
Jun 01, 1981
Accession Number
ADA103875

Entities

People

  • B. W. Silverman

Organizations

  • University of Wisconsin–Madison

Tags

Communities of Interest

  • C4I

DTIC Thesaurus Topics

  • Asymptotic Normality
  • Data Analysis
  • Data Science
  • Estimators
  • Functional Analysis
  • Gaussian Processes
  • Hilbert Space
  • Information Science
  • Mathematics
  • Normality
  • Probability
  • Probability Density Functions
  • Random Variables
  • Statistical Algorithms
  • Statistics
  • Stochastic Processes
  • United States

Fields of Study

  • Mathematics

Readers

  • Operations Research
  • Statistical inference.