We review several universal lower bounds on statistical estimation, including deterministic bounds on unbiased estimators such as Cramér-Rao bound and Barankin-type bound, as well as Bayesian bounds such as Ziv-Zakai bound. We present explicit forms of these bounds, illustrate their usage for parameter estimation in Gaussian additive noise, and compare their tightness.

A Cram er{Rao type bound for two{parameter quantum statistical model is studied, based on linear random measurements. It is shown that in nitely many (continuous potency) measurements which attain a lower bound exist. The RLD{bound for pure coherent models is shown to be most informative.

We present a new bound for the minimum distance of a general primary linear code. For affine variety codes defined from generalised Cab polynomials the new bound often improves dramatically on the Feng-Rao bound for primary codes [1, 10]. The method does not only work for the minimum distance but can be applied to any generalised Hamming weight.

A marginal version of the enumeration Bayesian Cramér-Rao Bound (EBCRB) for jump Markov systems is proposed. It is shown that the proposed bound is at least as tight as EBCRB and the improvement stems from better handling of the nonlinearities. The new bound is illustrated to yield tighter results than BCRB and EBCRB on a benchmark example.

We derived a new speed limit in population dynamics, which is fundamental on the evolutionary rate. By splitting contributions of selection and mutation to rate, we obtained bound arbitrary observables, named bound, that can be tighter than conventional Cram\'er-Rao bound. Remarkably, much if contribution more dominant mutation. This tightness geometrically characterized by correlation between ...

– We are concerned with the problem of tracking a single target using multiple sensors. At each stage the measurement number is uncertain and measurements can either be target generated or false alarms. The CramérRao bound gives a lower bound on the performance of any unbiased estimator of the target state. In this paper we build on earlier research concerned with calculating Posterior Cramér-R...

In this letter it is shown that similar to the Cramér-Rao lower bound (CRLB), the functional transformation property also holds for the modified CRLB (MCRLB).

We present a parameter retrieval method which incorporates prior knowledge about the object into ptychography. The proposed is applied to two applications: (1) of small particles from Fourier ptychographic dark field measurements; (2) rectangular structure with real-space influence Poisson noise discussed in second part paper. Cramér Rao Lower Bound both applications computed and Monte Carlo an...

The goal of this contribution is to characterize the best achievable mean-squared error (MSE) in estimating a sparse deterministic parameter from measurements corrupted by Gaussian noise. To this end, an appropriate definition of bias in the sparse setting is developed, and the constrained Cramér–Rao bound (CRB) is obtained. This bound is shown to equal the CRB of an estimator with knowledge of...

Non-Bayesian parameter estimation under parametric constraints is encountered in numerous applications in signal processing, communications, and control. Mean-squared-error (MSE) lower bounds are widely used as performance benchmarks and for system design. The well-known constrained Cramér-Rao bound (CCRB) is a lower bound on the MSE of estimators that satisfy some unbiasedness conditions. In m...