Moment inequality for quadratic forms of random vectors is of particular interest in covariance matrix testing and estimation problems. In this paper, we prove a Rosenthal-type inequality, which exhibits new features and certain improvement beyond the unstructured Rosenthal inequality of quadratic forms when dimension of the vectors increases without bound. Applications to test the block diagon...

This paper considers local convergence of secant methods for a nonlinear system of equations. The well-known local convergence theory has been developed by Broyden, Dennis and Moré (1973). They used a norm inequality such that the difference between two vectors transformed by some matrix is bounded above by an order of one of the two. Instead, in the present paper, we use an inequality that bou...

Bounds on distances or similarity measures can be useful to help search large databases efficiently. Here we consider the case of large databases of small molecules represented by molecular fingerprint vectors with the Tanimoto similarity measure. We derive a new intersection inequality which provides a bound on the Tanimoto similarity between two fingerprint vectors and show that this bound is...

We study the antieigenvectors of the generalized eigenvalue problem Af = λBf by using the concept of stationary vectors and then obtain an operator inequality complementary to Schwarz’s inequality in Hilbert space. AMS Mathematics Subject Classification (2000): 47A63,47A75

It is well known that there is a one-to-one correspondence between the entropy vector of a collection of n random variables and a certain group-characterizable vector obtained from a finite group and n of its subgroups [1]. However, if one restricts attention to abelian groups then not all entropy vectors can be obtained. This is an explanation for the fact shown by Dougherty et al [2] that lin...