Unified extension of variance bounds for integrated Pearson family

被引：3

作者：

Afendras, Giorgos ^{[1
,2
]}

机构：

[1] Univ Athens, Sect Stat, Dept Math, Athens 15784, Greece

[2] Univ Athens, OR, Athens 15784, Greece

来源：

ANNALS OF THE INSTITUTE OF STATISTICAL MATHEMATICS | 2013年 / 65卷 / 04期

关键词：

Completeness; Derivatives of higher order; Fourier coefficients; Orthogonal polynomials; Parseval identity; Pearson family of distributions; Rodrigues-type formula; Variance bounds; INEQUALITIES; DISTRIBUTIONS;

D O I：

10.1007/s10463-012-0388-3

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

We use some properties of orthogonal polynomials to provide a class of upper/lower variance bounds for a function of an absolutely continuous random variable , in terms of the derivatives of up to some order. The new bounds are better than the existing ones.

引用

页码：687 / 702

页数：16

共 23 条

[1] An extended Stein-type covariance identity for the Pearson family wit a applications to lower variance bounds [J].

Afendras, G. ;

Papadatos, N. ;

Papathanasiou, V. .

BERNOULLI, 2011, 17 (02) :507-529

[2]

Afendras G., 2012, ARXIV11071754V3

[3]

Afendras G., 2012, ARXIV12052903V1

[4]

[Anonymous], 1993, Continuous Univariate Distributions, DOI DOI 10.1016/0167-9473(96)90015-8

[5]

[Anonymous], 2006, STAT METHODOL

[6] ON EXTENSIONS OF BRUNN-MINKOWSKI AND PREKOPA-LEINDLER THEOREMS, INCLUDING INEQUALITIES FOR LOG CONCAVE FUNCTIONS, AND WITH AN APPLICATION TO DIFFUSION EQUATION [J].

BRASCAMP, HJ ;

LIEB, EH .

JOURNAL OF FUNCTIONAL ANALYSIS, 1976, 22 (04) :366-389

[7] ON UPPER AND LOWER BOUNDS FOR THE VARIANCE OF A FUNCTION OF A RANDOM VARIABLE [J].

CACOULLOS, T .

ANNALS OF PROBABILITY, 1982, 10 (03) :799-809

[8] ON UPPER-BOUNDS FOR THE VARIANCE OF FUNCTIONS OF RANDOM-VARIABLES [J].

CACOULLOS, T ;

PAPATHANASIOU, V .

STATISTICS & PROBABILITY LETTERS, 1985, 3 (04) :175-184

[9]

Cacoullos T., 1989, STAT DATA ANAL INFER, P239

[10]

Charalambides CA., 2002, Enumerative combinatorics

← 1 2 3 →