Maximum Likelihood Estimation for Stationary Point Processes.

Abstract

In this paper we derive the log likelihood function for point processes in terms of their stochastic intensities, using the martingale approach. For practical purposes we work with an approximate log likelihood function which is shown to possess the usual asymptotic properties of a log likelihood function. The resulting estimates are strongly consistent and asymptotically normal (under some regularity conditions). As a by-product, a strong law of large numbers and a central limit theorem for continuous martingale are derived. (Author)

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Document Details

Document Type
Technical Report
Publication Date
Aug 01, 1980
Accession Number
ADA089117

Entities

People

  • Madan L. Puri
  • Pham-dinh Tuan

Organizations

  • Indiana University Bloomington

Tags

Communities of Interest

  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Air Force
  • Algorithms
  • Computations
  • Convergence
  • Inequalities
  • Integrals
  • Intensity
  • Mathematics
  • Maximum Likelihood Estimation
  • New York
  • Probability
  • Probability Distributions
  • Random Variables
  • Security
  • Stationary
  • Statistics
  • Stochastic Processes

Fields of Study

  • Mathematics

Readers

  • Mathematical Modeling and Probability Theory.
  • Regression Analysis.