State Estimation for Cox Processes with Unknown Law: Parametric Models.

Abstract

Let (N sub i, M sub i) be i.i.d. copies of a Cox pair (N,M), with the Cox processes N sub i, but not the directing measures M Sub i, observable. Suppose that the probability law of (N,M) belongs to a finite-dimensional parametric family sub theta but is otherwise unknown. Approximations are derived for state estimators. Under standard smoothness and reqularity assumptions n times the difference between the ture and pseduo-stae estimators converges in distribution to a Gaussian random measure, with respect to the variation norm topology. Computation of maximum likelihood estimators by the EM algorithm is discussed in general and for two specific examples. Keywords: Parametric statistical model; Maximum likelihood estimator; EM algorithm.

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Document Details

Document Type
Technical Report
Publication Date
Nov 01, 1985
Accession Number
ADA166179

Entities

People

  • Alan F. Karr

Organizations

  • Johns Hopkins University

Tags

Communities of Interest

  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Abstracts
  • Algorithms
  • Classification
  • Computational Complexity
  • Computations
  • Estimators
  • Mathematical Analysis
  • Mathematics
  • Monitoring
  • Notation
  • Probability
  • Procurement
  • Security
  • Standards
  • Three Dimensional

Fields of Study

  • Mathematics

Readers

  • Statistical inference.