The Cramer-Rao Lower Bound is widely used in statistical signal processing as a benchmark to evaluate unbiased estimators. However, for some random variables, the probability density function has no closed analytical form. Therefore, it is very hard or impossible to evaluate the Cramer-Rao Lower Bound directly. In these cases the characteristic function may still have a closed and even simple f...

This article focuses on an important piece of work of the world renowned Indian statistician, Calyampudi Radhakrishna Rao. In 1945, C. R. Rao (25 years old then) published a pathbreaking paper [43], which had a profound impact on subsequent statistical research. Roughly speaking, Rao obtained a lower bound to the variance of an estimator. The importance of this work can be gauged, for instance,...

A fundamental issue in NMR spectroscopy is the estimation of parameters such as the Larmor frequencies of nuclei, J coupling constants, and relaxation rates. The Cramer-Rao lower bound provides a method to assess the best achievable accuracy of parameter estimates resulting from an unbiased estimation procedure. We show how the Cramer-Rao lower bound can be calculated for data obtained from mul...

As an application of the improved Cauchy-Schwartz inequality due to Walker (Statist. Probab. Lett. (2017) 122:86-90), we obtain an improved version of the Cramer-Rao inequality for randomly censored data derived by Abdushukurov and Kim (J. Soviet. Math. (1987) pp. 2171-2185). We derive a lower bound of Bhattacharya type for the mean square error of a parametric function based on randomly censor...

-In this paper we present new approximation expressions for the Cramer-Rao Lower Bound on unbiased estimates of frequency, phase, amplitude and DC offset for uniformly sampled signal embedded in white-Gaussian noise. This derivation is based on well-known assumptions and a novel set of approximations for finite series of trigonometric functions. The estimated Cramer-Rao Lower Bounds are given i...