The paper considers a family of probability distributions depending on a parameter. The goal is to derive the generalized versions of Cramér-Rao and Bhattacharyya inequalities for the weighted covariance matrix and of the Kullback inequality for the weighted Kullback distance, which are important objects themselves [9, 23, 28]. The asymptotic forms of these inequalities for a particular family ...

assuming of course that the covariance exists. The infinite sequence {Xn, n ≥ 1} is said to be associated if every finite subfamily is associated. The concept of association was introduced by Esary et al. [1]. There are some results on the strong law of large numbers for associated sequences. Rao [4] developed the Hajek-Renyi inequality for associated sequences and proved the following theorem....

This paper investigates the linear separation requirements for Angle-of-Arrival (AoA) and range sensors, in order to achieve the optimal performance in estimating the position of a target from multiple and typically noisy sensor measurements. We analyse the sensor-target geometry in terms of the Cramer-Rao inequality and the corresponding Fisher information matrix, in order to characterize loca...

We introduce the Fisher's information of degree q, q e 2/V*, of a given random variable X, with a density function depending on a parameter 0, 6 e 0, the average Fisher's information of this variable when the parameter is itself random, and the logarithmic information of degree q which characterizes this one. We exhibit relations concerning these 3 quantities and we more particularly obtain ext...

A large body of literature exists across different contexts on unequal societal role burdens experienced by the different sexes (Cornwall, Harrison & Whitehead, 2007; Faust, 2013; Jacobs, 1996; Kabeer, 2005; Powell, 2005; Rao, 2006; Rao & Kelleher, 2003; Smyth, 2007; Unterhalter & North, 2011; Wendoh & Wallace, 2005), as well as in the South African context (Geisler, 2000; Hassim, 2006; McEwan,...

The emergence of persistent political hierarchy and economic inequality beginning about eleven thousand years ago may be explained in part by the novel equilibrium network structures that post-Pleistocene ecological and economic conditions supported. I explore how changes in the nature of wealth and the division of labor could have induced transitions among three stable network structures: symm...

In this note, we provide several characterizations of regular local rings in positive characteristics, in terms of the Hilbert-Kunz multiplicity and its higher Tor counterparts ti = lim n→∞ l(Tori(k, f n R))/p . We also apply the characterizations to improve a recent result by Bridgeland and Iyengar in the characteristic p case. Our proof avoids using the existence of big CohenMacaulay modules,...