DeepAI AI Chat
Log In Sign Up

Barankin-Type Bound for Constrained Parameter Estimation

by   Eyal Nitzan, et al.
Ben-Gurion University of the Negev

In constrained parameter estimation, the classical constrained Cramer-Rao bound (CCRB) and the recent Lehmann-unbiased CCRB (LU-CCRB) are lower bounds on the performance of mean-unbiased and Lehmann-unbiased estimators, respectively. Both the CCRB and the LU-CCRB require differentiability of the likelihood function, which can be a restrictive assumption. Additionally, these bounds are local bounds that are inappropriate for predicting the threshold phenomena of the constrained maximum likelihood (CML) estimator. The constrained Barankin-type bound (CBTB) is a nonlocal mean-squared-error (MSE) lower bound for constrained parameter estimation that does not require differentiability of the likelihood function. However, this bound requires a restrictive mean-unbiasedness condition in the constrained set. In this work, we propose the Lehmann-unbiased CBTB (LU-CBTB) on the weighted MSE. This bound does not require differentiability of the likelihood function and assumes Lehmann-unbiasedness, which is less restrictive than the CBTB mean-unbiasedness. We show that the LU-CBTB is tighter than or equal to the LU-CCRB and coincides with the CBTB for linear constraints. For nonlinear constraints the LU-CBTB and the CBTB are different and the LU-CBTB can be a lower bound on the WMSE of constrained estimators in cases, where the CBTB is not. In the simulations, we consider direction-of-arrival estimation of an unknown constant modulus discrete signal. In this case, the likelihood function is not differentiable and constrained Cramer-Rao-type bounds do not exist, while CBTBs exist. It is shown that the LU-CBTB better predicts the CML estimator performance than the CBTB, since the CML estimator is Lehmann-unbiased but not mean-unbiased.


New Cramer-Rao-Type Bound for Constrained Parameter Estimation

Non-Bayesian parameter estimation under parametric constraints is encoun...

Constrained Best Linear Unbiased Estimation

The least squares (LS) estimator and the best linear unbiased estimator ...

A Two-Stage Batch Algorithm for Nonlinear Static Parameter Estimation

A two-stage batch estimation algorithm for solving a class of nonlinear,...

Non-Bayesian Post-Model-Selection Estimation as Estimation Under Model Misspecification

In many parameter estimation problems, the exact model is unknown and is...

Sequential Estimation under Multiple Resources: a Bandit Point of View

The problem of Sequential Estimation under Multiple Resources (SEMR) is ...

Functional Properties of the Ziv-Zakai bound with Arbitrary Inputs

This paper explores the Ziv-Zakai bound (ZZB), which is a well-known Bay...