IEEE transactions on information theory, ISSN 1557-9654, 2018, Volume 64, Issue 2, pp. 1083 - 1091

In this paper, we introduce new Stein identities for gamma target distribution as well as a new non-linear channel specifically designed for gamma inputs. From...

Additives | Channel estimation | Estimation theory | relative entropy | Entropy | Random variables | Non-linear channel | Mutual information | Standards | Fisher information | Relative entropy | STEINS METHOD | estimation theory | BOUNDS | COMPUTER SCIENCE, INFORMATION SYSTEMS | LIMIT | mutual information | RANDOM-VARIABLES | ENGINEERING, ELECTRICAL & ELECTRONIC | Random noise theory | Usage | Stochastic processes | Random noise | Lattice theory | Entropy (Information theory) | Communication channels

Additives | Channel estimation | Estimation theory | relative entropy | Entropy | Random variables | Non-linear channel | Mutual information | Standards | Fisher information | Relative entropy | STEINS METHOD | estimation theory | BOUNDS | COMPUTER SCIENCE, INFORMATION SYSTEMS | LIMIT | mutual information | RANDOM-VARIABLES | ENGINEERING, ELECTRICAL & ELECTRONIC | Random noise theory | Usage | Stochastic processes | Random noise | Lattice theory | Entropy (Information theory) | Communication channels

Journal Article

Statistics and Probability Letters, ISSN 0167-7152, 04/2016, Volume 111, pp. 67 - 71

We present a general characterization theorem for parametric probability distributions in terms of a differential operator akin to the so-called Stein...

Parametric distributions | Stein’s method | Stein operators | Stein's method | Analysis | Distribution (Probability theory)

Parametric distributions | Stein’s method | Stein operators | Stein's method | Analysis | Distribution (Probability theory)

Journal Article

Probability surveys, ISSN 1549-5787, 2017, Volume 14, Issue 2017, pp. 1 - 52

Journal Article

Journal of mathematical analysis and applications, ISSN 0022-247X, 2019, Volume 469, Issue 1, pp. 260 - 279

We build upon recent advances on the distributional aspect of Stein's method to propose a novel and flexible technique for computing Stein operators for random...

Variance-gamma distribution | Product distributions | Stein's method | Stein operators | GAMMA | MATHEMATICS | RATES | MATHEMATICS, APPLIED | APPROXIMATION | PRODUCTS | RANDOM-VARIABLES | BETA

Variance-gamma distribution | Product distributions | Stein's method | Stein operators | GAMMA | MATHEMATICS | RATES | MATHEMATICS, APPLIED | APPROXIMATION | PRODUCTS | RANDOM-VARIABLES | BETA

Journal Article

Stochastic Processes and their Applications, ISSN 0304-4149, 11/2017, Volume 127, Issue 11, pp. 3661 - 3688

We provide the first in-depth study of the Laguerre interpolation scheme between an arbitrary probability measure and the gamma distribution. We propose new...

Representation formulae | Gamma approximation | Smart path | Semigroup interpolation | Entropy | De Bruijn identity | Fisher information | INEQUALITIES | STATISTICS & PROBABILITY | CENTRAL-LIMIT-THEOREM

Representation formulae | Gamma approximation | Smart path | Semigroup interpolation | Entropy | De Bruijn identity | Fisher information | INEQUALITIES | STATISTICS & PROBABILITY | CENTRAL-LIMIT-THEOREM

Journal Article

Annals of the Institute of Statistical Mathematics, ISSN 0020-3157, 2/2017, Volume 69, Issue 1, pp. 39 - 62

...Ann Inst Stat Math (2017) 69:39–62 DOI 10.1007/s10463-015-0533-x Efﬁcient ANOV A for directional data Christophe Ley 1 · Yvik Swan 2 · Thomas Verdebout 1...

Local asymptotic normality | Directional statistics | Statistics for Business/Economics/Mathematical Finance/Insurance | ANOVA | Statistics, general | Pseudo-FvML tests | Statistics | Rank-based inference | MEAN DIRECTIONS | COMMON PRINCIPAL COMPONENTS | SPHERE | STATISTICS & PROBABILITY | CIRCLE | FAMILY | DISTRIBUTIONS | FOLD TEST | R-ESTIMATION | PALEOMAGNETISM | RANK-TESTS | Monte Carlo method | Analysis | Studies | Mathematical models | Mathematics | Variance analysis | Monte Carlo methods | Computer simulation | Asymptotic properties | Mathematical analysis | Computational efficiency | Analysis of variance | Optimization | Symmetry

Local asymptotic normality | Directional statistics | Statistics for Business/Economics/Mathematical Finance/Insurance | ANOVA | Statistics, general | Pseudo-FvML tests | Statistics | Rank-based inference | MEAN DIRECTIONS | COMMON PRINCIPAL COMPONENTS | SPHERE | STATISTICS & PROBABILITY | CIRCLE | FAMILY | DISTRIBUTIONS | FOLD TEST | R-ESTIMATION | PALEOMAGNETISM | RANK-TESTS | Monte Carlo method | Analysis | Studies | Mathematical models | Mathematics | Variance analysis | Monte Carlo methods | Computer simulation | Asymptotic properties | Mathematical analysis | Computational efficiency | Analysis of variance | Optimization | Symmetry

Journal Article

IEEE Transactions on Information Theory, ISSN 0018-9448, 09/2013, Volume 59, Issue 9, pp. 5584 - 5591

Pinsker's inequality states that the relative entropy between two random variables X and Y dominates the square of the total variation distance between X and...

Measurement | Discrete density approach | Pinsker inequality | Poisson approximation | Entropy | scaled Fisher information | Approximation methods | Stein characterizations | Equations | Standards | Cramer-Rao bounds | Random variables | total variation distance | INFORMATION | COMPUTER SCIENCE, INFORMATION SYSTEMS | CENTRAL-LIMIT-THEOREM | ENTROPY | ENGINEERING, ELECTRICAL & ELECTRONIC | Usage | Entropy (Information theory) | Analysis | Geometric probabilities | Research | Poisson distribution | Probabilities | Combinatorial probabilities

Measurement | Discrete density approach | Pinsker inequality | Poisson approximation | Entropy | scaled Fisher information | Approximation methods | Stein characterizations | Equations | Standards | Cramer-Rao bounds | Random variables | total variation distance | INFORMATION | COMPUTER SCIENCE, INFORMATION SYSTEMS | CENTRAL-LIMIT-THEOREM | ENTROPY | ENGINEERING, ELECTRICAL & ELECTRONIC | Usage | Entropy (Information theory) | Analysis | Geometric probabilities | Research | Poisson distribution | Probabilities | Combinatorial probabilities

Journal Article

Stochastic processes and their applications, ISSN 0304-4149, 2019, Volume 129, Issue 7, pp. 2341 - 2375

We provide a bound on a distance between finitely supported elements and general elements of the unit sphere of ℓ2(N∗). We use this bound to estimate the...

Stein discrepancy | Variance-gamma distribution | Malliavin Calculus | Second Wiener chaos | Wasserstein-2 distance | DISTRIBUTIONS | STEINS METHOD | LIMIT-THEOREMS | PRODUCTS | STATISTICS & PROBABILITY

Stein discrepancy | Variance-gamma distribution | Malliavin Calculus | Second Wiener chaos | Wasserstein-2 distance | DISTRIBUTIONS | STEINS METHOD | LIMIT-THEOREMS | PRODUCTS | STATISTICS & PROBABILITY

Journal Article

Statistica Sinica, ISSN 1017-0405, 1/2013, Volume 23, Issue 1, pp. 305 - 332

In this paper, we provide R-estimators of the location of a rotationally symmetric distribution on the unit sphere of ℝk. In order to do so we first prove the...

Preliminary estimates | Asymptotic properties | Sine function | General | Parameterization | Rotation | Estimators | Consistent estimators | Fisher information | Jacobians | Estimation methods | Local asymptotic normality | Spherical statistics | R-estimation | Rank-based methods | TESTS | SPHERES | GROUP MODELS | STATISTICS & PROBABILITY | ADAPTIVE ESTIMATION | spherical statistics | ARMA PROCESSES | rank-based methods | SHAPE | TREND | RANK-BASED INFERENCE

Preliminary estimates | Asymptotic properties | Sine function | General | Parameterization | Rotation | Estimators | Consistent estimators | Fisher information | Jacobians | Estimation methods | Local asymptotic normality | Spherical statistics | R-estimation | Rank-based methods | TESTS | SPHERES | GROUP MODELS | STATISTICS & PROBABILITY | ADAPTIVE ESTIMATION | spherical statistics | ARMA PROCESSES | rank-based methods | SHAPE | TREND | RANK-BASED INFERENCE

Journal Article

Journal of Functional Analysis, ISSN 0022-1236, 03/2014, Volume 266, Issue 5, pp. 3170 - 3207

We develop a new method for bounding the relative entropy of a random vector in terms of its Stein factors. Our approach is based on a novel representation for...

Carbery–Wright inequality | Stein factors | Central limit theorem | Relative entropy | Gaussian fields | de Bruijnʼs formula | Fisher information | Fourth moment theorem | De Bruijn's formula | Carbery-Wright inequality | STEINS METHOD | INEQUALITIES | MULTIVARIATE NORMAL APPROXIMATION | de Bruijn's formula | CENTRAL LIMIT-THEOREMS | MATHEMATICS | CHAOS | FLUCTUATIONS | CONVERGENCE | Probability | Mathematics | Information Theory | Computer Science

Carbery–Wright inequality | Stein factors | Central limit theorem | Relative entropy | Gaussian fields | de Bruijnʼs formula | Fisher information | Fourth moment theorem | De Bruijn's formula | Carbery-Wright inequality | STEINS METHOD | INEQUALITIES | MULTIVARIATE NORMAL APPROXIMATION | de Bruijn's formula | CENTRAL LIMIT-THEOREMS | MATHEMATICS | CHAOS | FLUCTUATIONS | CONVERGENCE | Probability | Mathematics | Information Theory | Computer Science

Journal Article

The Annals of applied probability, ISSN 1050-5164, 2017, Volume 27, Issue 1, pp. 216 - 241

this paper, we propose tight upper and lower bounds for the Wasser-stein distance between any two univariate continuous distributions with probability...

Prior distribution | Bayesian analysis | Stein's method | Posterior distribution | DISTRIBUTIONS | prior distribution | STEINS METHOD | posterior distribution | STATISTICS & PROBABILITY

Prior distribution | Bayesian analysis | Stein's method | Posterior distribution | DISTRIBUTIONS | prior distribution | STEINS METHOD | posterior distribution | STATISTICS & PROBABILITY

Journal Article

Bernoulli, ISSN 1350-7265, 5/2014, Volume 20, Issue 2, pp. 775 - 802

A famous characterization theorem due to C.F. Gauss states that the maximum likelihood estimator (MLE) of the parameter in a location family is the sample mean...

Maximum likelihood estimation | Gaussian distributions | Mathematical theorems | Sample size | Statistical theories | Sample mean | Random variables | Statistics | Probabilities | Perceptual localization | Maximum likelihood estimator | Minimal necessary sample size | Location parameter | One-parameter group family | Scale parameter | Score function | LOCATION | score function | STATISTICS | PROPERTY | scale parameter | one-parameter group family | STATISTICS & PROBABILITY | location parameter | maximum likelihood estimator | PROBABILITY | minimal necessary sample size | MODELS | EXPONENTIAL-FAMILIES | ESTIMATORS

Maximum likelihood estimation | Gaussian distributions | Mathematical theorems | Sample size | Statistical theories | Sample mean | Random variables | Statistics | Probabilities | Perceptual localization | Maximum likelihood estimator | Minimal necessary sample size | Location parameter | One-parameter group family | Scale parameter | Score function | LOCATION | score function | STATISTICS | PROPERTY | scale parameter | one-parameter group family | STATISTICS & PROBABILITY | location parameter | maximum likelihood estimator | PROBABILITY | minimal necessary sample size | MODELS | EXPONENTIAL-FAMILIES | ESTIMATORS

Journal Article

Electronic Communications in Probability, ISSN 1083-589X, 01/2013, Volume 18, pp. 1 - 14

We provide a new perspective on Stein's so-called density approach by introducing a new operator and characterizing class which are valid for a much wider...

Probability metrics | Magic factors | Stein's density approach | Generalized Fisher information | Pinsker's inequality | APPROXIMATION | magic factors | STATISTICS & PROBABILITY | ORTHOGONAL POLYNOMIALS | generalized Fisher information | probability metrics | VARIANCE BOUNDS | CENTRAL-LIMIT-THEOREM | ENTROPY

Probability metrics | Magic factors | Stein's density approach | Generalized Fisher information | Pinsker's inequality | APPROXIMATION | magic factors | STATISTICS & PROBABILITY | ORTHOGONAL POLYNOMIALS | generalized Fisher information | probability metrics | VARIANCE BOUNDS | CENTRAL-LIMIT-THEOREM | ENTROPY

Journal Article

Journal of Econometrics, ISSN 0304-4076, 02/2013, Volume 172, Issue 2, pp. 195 - 204

Classical estimation techniques for linear models either are inconsistent, or perform rather poorly, under α-stable error densities; most of them are not even...

Local asymptotic normality | LAD estimation | R-estimation | Stable distributions | Asymptotic relative efficiency | REGRESSION | TESTS | INFERENCE | DISTRIBUTIONS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | DENSITIES | SOCIAL SCIENCES, MATHEMATICAL METHODS | ECONOMICS | PARAMETER

Local asymptotic normality | LAD estimation | R-estimation | Stable distributions | Asymptotic relative efficiency | REGRESSION | TESTS | INFERENCE | DISTRIBUTIONS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | DENSITIES | SOCIAL SCIENCES, MATHEMATICAL METHODS | ECONOMICS | PARAMETER

Journal Article

Bernoulli, ISSN 1350-7265, 02/2019, Volume 25, Issue 1, pp. 89 - 111

Hall et al. [Phys. Rev. X 4 (2014) 041013] recently proposed that quantum theory can be understood as the continuum limit of a deterministic theory in which...

Stein’s method | Interacting particle system | Higher energy levels | Maxwell distribution | higher energy levels | DISTRIBUTIONS | RATES | Stein's method | interacting particle system | STATISTICS & PROBABILITY

Stein’s method | Interacting particle system | Higher energy levels | Maxwell distribution | higher energy levels | DISTRIBUTIONS | RATES | Stein's method | interacting particle system | STATISTICS & PROBABILITY

Journal Article

Studies in Applied Mathematics, ISSN 0022-2526, 10/2011, Volume 127, Issue 3, pp. 221 - 249

We consider two‐person sports where each rally is initiated by a server, the other player (the receiver) becoming the server when he/she wins a rally....

SQUASH | BADMINTON | MATHEMATICS, APPLIED | PROBABILITY | TENNIS | STRATEGY | RACQUETBALL

SQUASH | BADMINTON | MATHEMATICS, APPLIED | PROBABILITY | TENNIS | STRATEGY | RACQUETBALL

Journal Article

Periodica Mathematica Hungarica, ISSN 0031-5303, 12/2013, Volume 67, Issue 2, pp. 143 - 154

... SELF-NORMALIZED SUMS Siegfried H ormann 1 and Yvik Swan 2 1 D epartement de math ematique, Universit e libre de Bruxelles (ULB) Bd. Triomphe, CP210, Brussels...

heavy tails | normal approximation error | empirical correlation | Mathematics, general | Mathematics | Student t -statistic | 60F05 | self-normalized sums | Student t-statistic | DISTRIBUTIONS | MATHEMATICS | MATHEMATICS, APPLIED

heavy tails | normal approximation error | empirical correlation | Mathematics, general | Mathematics | Student t -statistic | 60F05 | self-normalized sums | Student t-statistic | DISTRIBUTIONS | MATHEMATICS | MATHEMATICS, APPLIED

Journal Article

Journal of applied probability, ISSN 0021-9002, 03/2009, Volume 46, Issue 1, pp. 1 - 18

Let X 1, X 2, …, X n be independent random variables uniformly distributed on [0,1]. We observe these sequentially and have to stop on exactly one of them. No...

Secretary problem | Optimal stopping | Poisson embedding | Robbins' problem | 60G40 | secretary problem

Secretary problem | Optimal stopping | Poisson embedding | Robbins' problem | 60G40 | secretary problem

Journal Article

09/2019

We build on the formalism developed in [arXiv:1906.08372v1] to propose new representations of solutions to Stein equations. We provide new uniform and non...

Mathematics - Probability

Mathematics - Probability

Journal Article

Journal of Applied Probability, ISSN 0021-9002, 3/2009, Volume 46, Issue 1, pp. 1 - 18

Let X₁, X₂,..., X n be independent random variables uniformly distributed on [0, 1]. We observe these sequentially and have to stop on exactly one of them. No...

Penalty function | Optimal strategies | Approximation | Differential equations | Losses incurred | Mathematical functions | Random variables | Poisson process | Asymptotic value | STATISTICS & PROBABILITY | Optimal stopping | Poisson embedding | secretary problem | Robbins' problem

Penalty function | Optimal strategies | Approximation | Differential equations | Losses incurred | Mathematical functions | Random variables | Poisson process | Asymptotic value | STATISTICS & PROBABILITY | Optimal stopping | Poisson embedding | secretary problem | Robbins' problem

Journal Article

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