A note on a variance bound for the multinomial and the negative multinomial distribution
We prove a Chernoff-type upper variance bound for the multinomial and the negative multinomial distribution. An application is also given.
math.PR↗
arXiv subjects
G. Afendras
Publications and source records attributed to G. Afendras.
Unified extension of variance bounds for integrated Pearson family
We use some properties of orthogonal polynomials to provide a class of upper/lower variance bounds for a function $g(X)$ of an absolutely continuous random variable $X$, in terms of the derivatives of $g$ up to some order. The new bounds are better than the existing ones.
math.PR↗
A factorial moment distance and an application to the matching problem
In this note we introduce the notion of factorial moment distance for non-negative integer-valued random variables and we compare it with the total variation distance. Furthermore, we study the rate of convergence in the classical matching problem and in a generalized matching distribution.
math.PR↗
Strengthened Chernoff-type variance bounds
Let $X$ be an absolutely continuous random variable from the integrated Pearson family and assume that $X$ has finite moments of any order. Using some properties of the associated orthonormal polynomial system, we provide a class of strengthened Chernoff-type variance bounds.
stat.ME↗
An extended Stein-type covariance identity for the Pearson family with applications to lower variance bounds
For an absolutely continuous (integer-valued) r.v. $X$ of the Pearson (Ord) family, we show that, under natural moment conditions, a Stein-type covariance identity of order $k$ holds (cf. [Goldstein and Reinert, J. Theoret. Probab. 18 (2005) 237--260]). This identity is closely related to the corresponding sequence of orthogonal polynomials, obtained by a Rodrigues-type formula, and provides convenient expressions for the Fourier coefficients of an arbitrary function. Application of the covariance identity yields some novel expressions for the corresponding lower variance bounds for a function of the r.v. $X$, expressions that seem to be known only in particular cases (for the Normal, see [Houdré and Kagan, J. Theoret. Probab. 8 (1995) 23--30]; see also [Houdré and Pérez-Abreu, Ann. Probab. 23 (1995) 400--419] for corresponding results related to the Wiener and Poisson processes). Some applications are also given.
math.ST↗
On matrix variance inequalities
Olkin and Shepp (2005, J. Statist. Plann. Inference, vol. 130, pp. 351--358) presented a matrix form of Chernoff's inequality for Normal and Gamma (univariate) distributions. We extend and generalize this result, proving Poincare-type and Bessel-type inequalities, for matrices of arbitrary order and for a large class of distributions.
stat.ME↗