Can the Cramér-Rao Lower Bound be constant?

1. What are the regularity conditions for Cramér-Rao inequality?
2. Can Cramer-Rao lower bound be negative?
3. Are cramér-Rao lower bounds an accurate estimate for standard deviations in in vivo magnetic resonance spectroscopy?
4. Why is the Cramer-Rao lower bound important?

What are the regularity conditions for Cramér-Rao inequality?

If W(X) is unbiased for τ(θ), then W(X) attains the Cramer-Rao lower bound if and only if ∂ ∂θ logL(θ|x) = Sn(x|θ) = a(θ)[W(X) − τ(θ)] for some function a(θ).

Can Cramer-Rao lower bound be negative?

If the data points are on average below the true population mean, then the score is negative.

Are cramér-Rao lower bounds an accurate estimate for standard deviations in in vivo magnetic resonance spectroscopy?

Abstract. Due to inherent time constraints for in vivo experiments, it is infeasible to repeat multiple MRS scans to estimate standard deviations on the desired measured parameters. As such, the Cramér-Rao lower bounds (CRLBs) have become the routine method to approximate standard deviations for in vivo experiments.

Why is the Cramer-Rao lower bound important?

One of the most important applications of the Cramer-Rao lower bound is that it provides the asymptotic optimality property of maximum likelihood estimators. The Cramer-Rao theorem involves the score function and its properties which will be derived first.