The moment-entropy inequality shows that a continuous random variable with given second moment and maximal Shannon entropy must be Gaussian. Stam’s inequality shows that a continuous random variable with given Fisher information and minimal Shannon entropy must also be Gaussian. The CramérRao inequality is a direct consequence of these two inequalities. In this paper the inequalities above are ...

In this paper, we obtain some matrix inequalities in Löwner partial ordering for Khatri-Rao products of positive semidefinite Hermitian matrices. Furthermore, we generalize the Oppenheim’s inequality, with which we will improve some recent results.

The aim of this paper is to show a simple way to construct asymptotic minimax lower bounds for risks based on different types of quadratic loss functions in semiparametric inference problems. For the sake of clarity, we consider the simple case of the state estimation of a dynamical system with small noise. The proofs are based on the van Trees inequality, namely an integral type Cramér-Rao ine...

The aim of this article is to show a simple way to construct asymptotic minimax lower bounds for risks based on different types of quadratic loss functions in semiparametric inference problems. For the sake of clarity, we consider the simple case of the state estimation of a dynamical system with small noise. The proofs are based on the van Trees inequality, namely, an integral-type Cramér-Rao ...

We first give an Oppenheim type determinantal inequality for the Khatri-Rao product of two block positive semidefinite matrices, and then we extend our result to multiple matrices. As products, extensions inequalities Hadamard are also included.

This paper addresses the problem of Doppler frequency estimation in the presence of speckle and receiver noise. An ultimate accuracy bound for Doppler frequency estimation is derived from the Cramer-Rao inequality. It is shown that estimates based on the correlation of the signal power spectra with an arbitrary weighting function are approximately Gaussian distributed. Their variance is derived...