The Annals of Statistics, ISSN 0090-5364, 06/2019, Volume 47, Issue 3, pp. 1616 - 1633

Journal Article

IEEE Transactions on Information Theory, ISSN 0018-9448, 09/2019, Volume 65, Issue 9, pp. 5294 - 5301

Upper bounds on absolute moments of the scores are derived for sums of independent random variables in terms of the moments of the scores, as well as in terms...

Score | Density measurement | Convolution | Stam’s inequality | Exponential distribution | score function | Random variables | total variation | Zinc | Convergence | Fisher information | Stam's inequality | COMPUTER SCIENCE, INFORMATION SYSTEMS | convolution | ENGINEERING, ELECTRICAL & ELECTRONIC

Score | Density measurement | Convolution | Stam’s inequality | Exponential distribution | score function | Random variables | total variation | Zinc | Convergence | Fisher information | Stam's inequality | COMPUTER SCIENCE, INFORMATION SYSTEMS | convolution | ENGINEERING, ELECTRICAL & ELECTRONIC

Journal Article

ANNALS OF STATISTICS, ISSN 0090-5364, 06/2019, Volume 47, Issue 3, pp. 1616 - 1633

Let F-n denote the distribution function of the normalized sum of n i.i.d. random variables. In this paper, polynomial rates of approximation of F n by the...

STATISTICS & PROBABILITY | Edgeworth approximations | Central limit theorem

STATISTICS & PROBABILITY | Edgeworth approximations | Central limit theorem

Journal Article

Journal of Theoretical Probability, ISSN 0894-9840, 12/2018, Volume 31, Issue 4, pp. 2390 - 2411

Let $$F_n$$ Fn denote the distribution function of the normalized sum $$Z_n = (X_1 + \cdots + X_n)/(\sigma \sqrt{n})$$ Zn=(X1+⋯+Xn)/(σn) of i.i.d. random...

Edgeworth expansions | Central limit theorem | Diophantine approximation | Probability Theory and Stochastic Processes | Mathematics | Statistics, general | 60F | STATISTICS & PROBABILITY

Edgeworth expansions | Central limit theorem | Diophantine approximation | Probability Theory and Stochastic Processes | Mathematics | Statistics, general | 60F | STATISTICS & PROBABILITY

Journal Article

Probability Surveys, ISSN 1549-5787, 2016, Volume 13, Issue 2016, pp. 57 - 88

Journal Article

Statistics and Probability Letters, ISSN 0167-7152, 07/2013, Volume 83, Issue 7, pp. 1644 - 1648

The central limit theorem is considered with respect to the transport distance . We discuss an alternative approach to a result of E. Rio, based on a...

Transport metrics | Berry-Esseen-type bounds | Central limit theorem

Transport metrics | Berry-Esseen-type bounds | Central limit theorem

Journal Article

IEEE Transactions on Information Theory, ISSN 0018-9448, 12/2017, Volume 63, Issue 12, pp. 7747 - 7752

An extension of the entropy power inequality to the form N r α (X + Y) ≥ N r α (X) + N r α (Y) with arbitrary independent summands X and Y in R n is obtained...

Heating systems | Power measurement | Density measurement | Rényi entropy | Entropy | Calculus | Electronic mail | Standards | Entropy power inequality | CONCAVITY | NASHS INEQUALITY | INFORMATION | COMPUTER SCIENCE, INFORMATION SYSTEMS | MONOTONICITY | Renyi entropy | CENTRAL-LIMIT-THEOREM | SIMPLE PROOF | ENGINEERING, ELECTRICAL & ELECTRONIC | Inequalities (Mathematics) | Usage | Entropy (Information theory) | Analysis

Heating systems | Power measurement | Density measurement | Rényi entropy | Entropy | Calculus | Electronic mail | Standards | Entropy power inequality | CONCAVITY | NASHS INEQUALITY | INFORMATION | COMPUTER SCIENCE, INFORMATION SYSTEMS | MONOTONICITY | Renyi entropy | CENTRAL-LIMIT-THEOREM | SIMPLE PROOF | ENGINEERING, ELECTRICAL & ELECTRONIC | Inequalities (Mathematics) | Usage | Entropy (Information theory) | Analysis

Journal Article

Probability Theory and Related Fields, ISSN 0178-8051, 2/2018, Volume 170, Issue 1, pp. 229 - 262

For sums of independent random variables $$S_n = X_1 + \cdots + X_n$$ S n = X 1 + ⋯ + X n , Berry–Esseen-type bounds are derived for the power transport...

Edgeworth expansions | Central limit theorem | Mathematical and Computational Biology | Statistics for Business/Economics/Mathematical Finance/Insurance | Theoretical, Mathematical and Computational Physics | Operations Research/Decision Theory | Probability Theory and Stochastic Processes | Mathematics | Transport distances | Coupling | 60F | Quantitative Finance | CONSTANTS | MINIMAL DISTANCES | STATISTICS & PROBABILITY | Transport | Independent variables | Random variables

Edgeworth expansions | Central limit theorem | Mathematical and Computational Biology | Statistics for Business/Economics/Mathematical Finance/Insurance | Theoretical, Mathematical and Computational Physics | Operations Research/Decision Theory | Probability Theory and Stochastic Processes | Mathematics | Transport distances | Coupling | 60F | Quantitative Finance | CONSTANTS | MINIMAL DISTANCES | STATISTICS & PROBABILITY | Transport | Independent variables | Random variables

Journal Article

Statistics and Probability Letters, ISSN 0167-7152, 07/2013, Volume 83, Issue 7, pp. 1644 - 1648

The central limit theorem is considered with respect to the transport distance . We discuss an alternative approach to a result of E. Rio, based on a...

Central limit theorem | Berry–Esseen-type bounds | Transport metrics

Central limit theorem | Berry–Esseen-type bounds | Transport metrics

Journal Article

Annali di Matematica Pura ed Applicata (1923 -), ISSN 0373-3114, 6/2016, Volume 195, Issue 3, pp. 681 - 695

The paper considers geometric lower bounds on the isoperimetric constant for logarithmically concave probability measures, extending and refining some results...

60E15 | 52A40 | Geometric functional inequalities | Logarithmically concave distributions | Mathematics, general | Mathematics | Isoperimetric inequalities | 46B09

60E15 | 52A40 | Geometric functional inequalities | Logarithmically concave distributions | Mathematics, general | Mathematics | Isoperimetric inequalities | 46B09

Journal Article

Electronic Communications in Probability, ISSN 1083-589X, 2015, Volume 20, pp. 1 - 12

Transport-entropy inequalities are considered in terms of Renyi informational divergence.

Optimal transport | Rényi informational divergence | Transport-entropy inequalities | STATISTICS & PROBABILITY | INEQUALITIES | transport-entropy inequalities | Renyi informational divergence

Optimal transport | Rényi informational divergence | Transport-entropy inequalities | STATISTICS & PROBABILITY | INEQUALITIES | transport-entropy inequalities | Renyi informational divergence

Journal Article

STATISTICS & PROBABILITY LETTERS, ISSN 0167-7152, 07/2013, Volume 83, Issue 7, pp. 1644 - 1648

The central limit theorem is considered with respect to the transport distance W-2. We discuss an alternative approach to a result of E. Rio, based on a...

Transport metrics | STATISTICS & PROBABILITY | COST | Central limit theorem | Berry-Esseen-type bounds

Transport metrics | STATISTICS & PROBABILITY | COST | Central limit theorem | Berry-Esseen-type bounds

Journal Article

Statistics & Probability Letters, ISSN 0167-7152, 07/2013, Volume 83, Issue 7, pp. 1644 - 1648

Journal Article

IEEE Transactions on Information Theory, ISSN 0018-9448, 02/2015, Volume 61, Issue 2, pp. 708 - 714

The classical entropy power inequality is extended to the Rényi entropy. We also discuss the question of the existence of the entropy for sums of independent...

entropy power inequality | Atmospheric measurements | Tin | Particle measurements | Educational institutions | Entropy | Vectors | Random variables | Renyi entropy | CONVERSE | COMPUTER SCIENCE, INFORMATION SYSTEMS | PROOF | YOUNGS-INEQUALITY | ENGINEERING, ELECTRICAL & ELECTRONIC | Random noise theory | Usage | Innovations | Information theory

entropy power inequality | Atmospheric measurements | Tin | Particle measurements | Educational institutions | Entropy | Vectors | Random variables | Renyi entropy | CONVERSE | COMPUTER SCIENCE, INFORMATION SYSTEMS | PROOF | YOUNGS-INEQUALITY | ENGINEERING, ELECTRICAL & ELECTRONIC | Random noise theory | Usage | Innovations | Information theory

Journal Article

06/2009

Annals of Probability 2009, Vol. 37, No. 2, 403-427 Brascamp--Lieb-type, weighted Poincar\'{e}-type and related analytic inequalities are studied for...

Mathematics - Probability

Mathematics - Probability

Journal Article

Probability Theory and Related Fields, ISSN 0178-8051, 5/2010, Volume 147, Issue 1, pp. 303 - 332

Isotropy-like properties are considered for finite measures with heavy tails. As a basic tool, we extend K. Ball’s relationship between convex bodies and...

Secondary 46xx | Isotropic convex bodies | Floating bodies | Primary 60xx | Statistics for Business/Economics/Mathematical Finance/Insurance | Operations Research/Decision Theory | Theoretical, Mathematical and Computational Physics | Probability Theory and Stochastic Processes | Mathematics | Mathematical Biology in General | Convex measures | Quantitative Finance | CONCAVE FUNCTIONS | INEQUALITIES | PROBABILITY-MEASURES | DUALITY | STATISTICS & PROBABILITY | BRUNN-MINKOWSKI | Studies | Mathematical analysis

Secondary 46xx | Isotropic convex bodies | Floating bodies | Primary 60xx | Statistics for Business/Economics/Mathematical Finance/Insurance | Operations Research/Decision Theory | Theoretical, Mathematical and Computational Physics | Probability Theory and Stochastic Processes | Mathematics | Mathematical Biology in General | Convex measures | Quantitative Finance | CONCAVE FUNCTIONS | INEQUALITIES | PROBABILITY-MEASURES | DUALITY | STATISTICS & PROBABILITY | BRUNN-MINKOWSKI | Studies | Mathematical analysis

Journal Article

Probability Theory and Related Fields, ISSN 0178-8051, 8/2014, Volume 159, Issue 3, pp. 435 - 478

Berry–Esseen-type bounds for total variation and relative entropy distances to the normal law are established for the sums of non-i.i.d. random variables.

Berry–Esseen bounds | Entropic distance | Central limit theorem | Mathematical and Computational Biology | Statistics for Business/Economics/Mathematical Finance/Insurance | Theoretical, Mathematical and Computational Physics | Operations Research/Decision Theory | Primary 60E | Probability Theory and Stochastic Processes | Mathematics | Entropy | Quantitative Finance | Berry-Esseen bounds | TRANSPORTATION COST | INEQUALITIES | INFORMATION | STATISTICS & PROBABILITY | Studies | Theorems | Law | Random variables | Probability theory | Sums

Berry–Esseen bounds | Entropic distance | Central limit theorem | Mathematical and Computational Biology | Statistics for Business/Economics/Mathematical Finance/Insurance | Theoretical, Mathematical and Computational Physics | Operations Research/Decision Theory | Primary 60E | Probability Theory and Stochastic Processes | Mathematics | Entropy | Quantitative Finance | Berry-Esseen bounds | TRANSPORTATION COST | INEQUALITIES | INFORMATION | STATISTICS & PROBABILITY | Studies | Theorems | Law | Random variables | Probability theory | Sums

Journal Article

Journal of Mathematical Sciences, ISSN 1072-3374, 5/2009, Volume 159, Issue 1, pp. 47 - 53

Isoperimetric constants of product probability measures are known to have an almost dimension-free character. We propose a new proof based on certain...

Mathematics, general | Mathematics

Mathematics, general | Mathematics

Journal Article

Probability Theory and Related Fields, ISSN 0178-8051, 6/2014, Volume 159, Issue 1, pp. 1 - 59

An Edgeworth-type expansion is established for the relative Fisher information distance to the class of normal distributions of sums of i.i.d. random...

Entropic distance | Central limit theorem | Mathematical and Computational Biology | Statistics for Business/Economics/Mathematical Finance/Insurance | Theoretical, Mathematical and Computational Physics | Operations Research/Decision Theory | Primary 60E | Edgeworth-type expansions | Probability Theory and Stochastic Processes | Mathematics | Entropy | Quantitative Finance | STATISTICS & PROBABILITY | INEQUALITIES | Studies | Probability | Mathematical analysis | Theorems | Convolution | Random variables | Normal distribution | Probability theory | Sums

Entropic distance | Central limit theorem | Mathematical and Computational Biology | Statistics for Business/Economics/Mathematical Finance/Insurance | Theoretical, Mathematical and Computational Physics | Operations Research/Decision Theory | Primary 60E | Edgeworth-type expansions | Probability Theory and Stochastic Processes | Mathematics | Entropy | Quantitative Finance | STATISTICS & PROBABILITY | INEQUALITIES | Studies | Probability | Mathematical analysis | Theorems | Convolution | Random variables | Normal distribution | Probability theory | Sums

Journal Article

Communications in Contemporary Mathematics, ISSN 0219-1997, 10/2017, Volume 19, Issue 5, p. 1650058

Sharpened forms of the concentration of measure phenomenon for classes of functions on the sphere are developed in terms of Hessians of these functions.

Concentration of measure phenomenon | logarithmic Sobolev inequalities | MATHEMATICS | MATHEMATICS, APPLIED

Concentration of measure phenomenon | logarithmic Sobolev inequalities | MATHEMATICS | MATHEMATICS, APPLIED

Journal Article

No results were found for your search.

Cannot display more than 1000 results, please narrow the terms of your search.