A Theory of Cramer-Rao Bounds for Constrained Parametric Models

Abstract

A simple expression for the Cramer-Rao bound (CRB) is presented for the scenario of estimating parameters theta that are required to satisfy a differentiable constraint function f(theta). A proof of this constrained CRB (CCRB) is provided using the implicit function theorem, and the encompassing theory of the CCRB is proven in a similar manner. This theory includes connecting the CCRB to notions of identifiability of constrained parameters; the linear model under a linear constraint the constrained maximum likelihood problem, it's asymptotic properties and the method of scoring with constraints; and hypothesis testing. The value of the tools developed in this theory are then presented in the communications context for the convolutive mixture model and the calibrated array model.

Open PDF

Document Details

Document Type
Technical Report
Publication Date
Jan 01, 2010
Accession Number
ADA524078

Entities

People

  • Terrence J. Moore Jr.

Organizations

  • University of Maryland

Tags

Communities of Interest

  • C4I
  • Sensors

DTIC Thesaurus Topics

  • Algorithms
  • Angle Of Arrival
  • Asymptotic Normality
  • Code Division Multiple Access
  • Convex Sets
  • Data Science
  • Estimators
  • Geometry
  • Information Science
  • Maximum Likelihood Estimation
  • Probability
  • Random Variables
  • Signal Processing
  • Statistical Algorithms
  • Statistics
  • Theses
  • Transfer Functions

Fields of Study

  • Engineering

Readers

  • Adaptive Control and Estimation with Uncertainty in Dynamic Systems.
  • Fire Suppression Systems Design.
  • Statistical inference.