IEEE Transactions on Information Theory, ISSN 0018-9448, 11/2013, Volume 59, Issue 11, pp. 7711 - 7717

The stochastic multiarmed bandit problem is well understood when the reward distributions are sub-Gaussian. In this paper, we examine the bandit problem under...

stochastic multi-armed bandit | Robustness | Probability distribution | Random variables | Electronic mail | Indexes | regret bounds | Standards | Equations | Heavy-tailed distributions | robust estimators | LOCATION | ALGORITHM | COMPUTER SCIENCE, INFORMATION SYSTEMS | ENGINEERING, ELECTRICAL & ELECTRONIC | Gaussian distribution | Research | Stochastic processes | Analysis

stochastic multi-armed bandit | Robustness | Probability distribution | Random variables | Electronic mail | Indexes | regret bounds | Standards | Equations | Heavy-tailed distributions | robust estimators | LOCATION | ALGORITHM | COMPUTER SCIENCE, INFORMATION SYSTEMS | ENGINEERING, ELECTRICAL & ELECTRONIC | Gaussian distribution | Research | Stochastic processes | Analysis

Journal Article

Canadian journal of statistics, ISSN 0319-5724, 2018, Volume 46, Issue 2, pp. 279 - 297

.... A promising method of this type is the model averaged tail area (MATA) confidence interval put forward by Turek & Fletcher (2012...

MSC 2010: Primary 62F25 | minimum coverage probability | secondary 62P12 | model averaged confidence intervals | MATA confidence interval | REGRESSION | ESTIMATORS | STATISTICS & PROBABILITY | SELECTION | INFERENCE | Confidence intervals | Regression models | Uncertainty | Statistical analysis | Upper bounds | Coverage | Regression analysis | Bayesian analysis

MSC 2010: Primary 62F25 | minimum coverage probability | secondary 62P12 | model averaged confidence intervals | MATA confidence interval | REGRESSION | ESTIMATORS | STATISTICS & PROBABILITY | SELECTION | INFERENCE | Confidence intervals | Regression models | Uncertainty | Statistical analysis | Upper bounds | Coverage | Regression analysis | Bayesian analysis

Journal Article

Communications in Statistics - Theory and Methods, ISSN 0361-0926, 09/2014, Volume 43, Issue 18, pp. 3797 - 3811

The ratio of normal tail probabilities and the ratio of Student's t tail probabilities have gained an increased attention in statistics and related areas...

Lower bound | Student's t distribution | Upper bound | Normal distribution | Tail probability ratio | BOUNDING ORDINATE | AREA | MILLS RATIO | APPROXIMATIONS | INEQUALITY | STATISTICS & PROBABILITY | Probability | Ratios | Conduction | Paper | Upper bounds | Statistics

Lower bound | Student's t distribution | Upper bound | Normal distribution | Tail probability ratio | BOUNDING ORDINATE | AREA | MILLS RATIO | APPROXIMATIONS | INEQUALITY | STATISTICS & PROBABILITY | Probability | Ratios | Conduction | Paper | Upper bounds | Statistics

Journal Article

Statistics and Probability Letters, ISSN 0167-7152, 10/2017, Volume 129, pp. 12 - 16

We consider the problem of finding the optimal upper bound for the tail probability of a sum of k nonnegative, independent and identically distributed random variables with given mean x. For k...

I.i.d. random variables | Tail probability | Markov’s inequality | Markov's inequality | BOUNDS | HYPERGRAPHS | INEQUALITY | ERDOS | STATISTICS & PROBABILITY | MATCHINGS

I.i.d. random variables | Tail probability | Markov’s inequality | Markov's inequality | BOUNDS | HYPERGRAPHS | INEQUALITY | ERDOS | STATISTICS & PROBABILITY | MATCHINGS

Journal Article

Statistics & probability letters, ISSN 0167-7152, 2018, Volume 135, pp. 1 - 6

We give explicit bounds for the tail probabilities for sums of independent geometric or exponential variables, possibly with different parameters.

Exponential distribution | Geometric distribution | Tail bounds | STATISTICS & PROBABILITY

Exponential distribution | Geometric distribution | Tail bounds | STATISTICS & PROBABILITY

Journal Article

Advances in applied probability, ISSN 0001-8678, 12/2017, Volume 49, Issue 4, pp. 1037 - 1066

... d , with f some positive function. Using classical results we can establish the tail asymptotics of ℙ{Γ(ξ u ) > u} as u → ∞ with Γ(ξ u ) = sup t ∈ [0, T] d ξ u...

supremum of Gaussian random fields | generalized Piterbarg constant | uniform double-sum method | double maxima | stationary process | Fractional Brownian motion | PARISIAN RUIN | CONSTANTS | RUIN PROBABILITY | FRACTIONAL BROWNIAN-MOTION | STATISTICS & PROBABILITY | HORIZON | EXTREMES | ASYMPTOTICS | Functionals | Upper bounds | Maxima

supremum of Gaussian random fields | generalized Piterbarg constant | uniform double-sum method | double maxima | stationary process | Fractional Brownian motion | PARISIAN RUIN | CONSTANTS | RUIN PROBABILITY | FRACTIONAL BROWNIAN-MOTION | STATISTICS & PROBABILITY | HORIZON | EXTREMES | ASYMPTOTICS | Functionals | Upper bounds | Maxima

Journal Article

Proceedings of the American Mathematical Society, ISSN 0002-9939, 01/2018, Volume 146, Issue 1, pp. 413 - 419

We prove a dimension-free tail comparison between the Euclidean norms of sums of independent random vectors uniformly distributed in centred Euclidean spheres...

Tail comparison | Probability inequalities | Uniform distributions in Euclidean spheres | Bounds for tail probabilities | Gaussian random vectors | MATHEMATICS | MATHEMATICS, APPLIED | bounds for tail probabilities | uniform distributions in Euclidean spheres | tail comparison

Tail comparison | Probability inequalities | Uniform distributions in Euclidean spheres | Bounds for tail probabilities | Gaussian random vectors | MATHEMATICS | MATHEMATICS, APPLIED | bounds for tail probabilities | uniform distributions in Euclidean spheres | tail comparison

Journal Article

Journal of Combinatorial Theory, Series B, ISSN 0095-8956, 01/2020, Volume 140, pp. 98 - 146

.... Shortly afterwards, Janson and Ruciński developed an alternative inductive approach, which often gives comparable results for the upper tail P(X≥(1+ε)EX...

Upper tail | Large deviations | Tail estimates | Missing log | Concentration inequalities | NUMBER | INEQUALITIES | MULTIVARIATE POLYNOMIALS | SUBSETS | SMALL SUBGRAPHS | MATHEMATICS | BOUNDS | TRIANGLES

Upper tail | Large deviations | Tail estimates | Missing log | Concentration inequalities | NUMBER | INEQUALITIES | MULTIVARIATE POLYNOMIALS | SUBSETS | SMALL SUBGRAPHS | MATHEMATICS | BOUNDS | TRIANGLES

Journal Article

Journal of Statistical Physics, ISSN 0022-4715, 11/2018, Volume 173, Issue 3, pp. 736 - 745

.... In particular, the tail behavior of the degree distribution does not play the same crucial role for the size of the giant as it does for many other properties of the graph...

Configuration model | Physical Chemistry | Theoretical, Mathematical and Computational Physics | Component size | Quantum Physics | 05C80 | Physics | Statistical Physics and Dynamical Systems | Degree distribution | DISTANCES | COMPONENT | RANDOM GRAPHS | PHYSICS, MATHEMATICAL | Mathematics - Probability

Configuration model | Physical Chemistry | Theoretical, Mathematical and Computational Physics | Component size | Quantum Physics | 05C80 | Physics | Statistical Physics and Dynamical Systems | Degree distribution | DISTANCES | COMPONENT | RANDOM GRAPHS | PHYSICS, MATHEMATICAL | Mathematics - Probability

Journal Article

Journal of the Mathematical Society of Japan, ISSN 0025-5645, 2015, Volume 67, Issue 4, pp. 1413 - 1448

We prove upper bounds on the transition probabilities of random walks with i.i.d. random conductances with a polynomial lower tail near 0...

Markov chains | Percolation | Random environments | Random walk | Random conductances | MATHEMATICS | random walk | percolation | RANDOM-WALKS | random environments | random conductances | HEAT-KERNEL DECAY | QUENCHED INVARIANCE-PRINCIPLES | GAUSSIAN UPPER-BOUNDS

Markov chains | Percolation | Random environments | Random walk | Random conductances | MATHEMATICS | random walk | percolation | RANDOM-WALKS | random environments | random conductances | HEAT-KERNEL DECAY | QUENCHED INVARIANCE-PRINCIPLES | GAUSSIAN UPPER-BOUNDS

Journal Article

Statistica Sinica, ISSN 1017-0405, 7/2015, Volume 25, Issue 3, pp. 1133 - 1144

We consider the problem of estimating the tail index α of a distribution satisfying a (α,β...

Minimax | Estimation bias | Analytical estimating | Standard error | Estimators | Consistent estimators | Probabilities | Estimation methods | Oracles | Perceptron convergence procedure | Pareto-type distributions | Adaptive estimation | Extreme value index | Minimax optimal bounds | minimax optimal bounds | STATISTICS & PROBABILITY | SAMPLE FRACTION | INFERENCE | extreme value index

Minimax | Estimation bias | Analytical estimating | Standard error | Estimators | Consistent estimators | Probabilities | Estimation methods | Oracles | Perceptron convergence procedure | Pareto-type distributions | Adaptive estimation | Extreme value index | Minimax optimal bounds | minimax optimal bounds | STATISTICS & PROBABILITY | SAMPLE FRACTION | INFERENCE | extreme value index

Journal Article

Electronic Journal of Probability, ISSN 1083-6489, 2016, Volume 21

.... As corollaries of these results, optimal in a certain sense upper bounds on the left-tail probabilities P (S-n <= x...

Submartingales | Probability inequalities | Sums of random variables | Upper bounds | Martingales | Generalized moments | sums of random variables | submartingales | BOUNDS | probability inequalities | martingales | upper bounds | STATISTICS & PROBABILITY | generalized moments | PROBABILITY-INEQUALITIES | MOMENTS

Submartingales | Probability inequalities | Sums of random variables | Upper bounds | Martingales | Generalized moments | sums of random variables | submartingales | BOUNDS | probability inequalities | martingales | upper bounds | STATISTICS & PROBABILITY | generalized moments | PROBABILITY-INEQUALITIES | MOMENTS

Journal Article

Electronic Journal of Statistics, ISSN 1935-7524, 08/2015, Volume 9, Issue 2, pp. 2751 - 2792

This paper presents an adaptive version of the Hill estimator based on Lespki's model selection method. This simple data-driven index selection method is shown...

Lepski’s method | Adaptivity | Order statistics | Concentration inequalities | Hill estimator | Lepski's method | order statistics | EXTREME | adaptivity | LOWER BOUNDS | STATISTICS & PROBABILITY | concentration inequalities | SAMPLE FRACTION | INFERENCE | SUP-NORM | SUMS | Probability | Mathematics

Lepski’s method | Adaptivity | Order statistics | Concentration inequalities | Hill estimator | Lepski's method | order statistics | EXTREME | adaptivity | LOWER BOUNDS | STATISTICS & PROBABILITY | concentration inequalities | SAMPLE FRACTION | INFERENCE | SUP-NORM | SUMS | Probability | Mathematics

Journal Article

Random Structures & Algorithms, ISSN 1042-9832, 08/2015, Volume 47, Issue 1, pp. 99 - 108

...: for any ε > 0 , the probability that the fraction of variables that occur exceeds the expectation by more than ε is bounded by P r [ Y 1 + … + Y r ≥ ( p + ε ) r ] ≤ e...

Chernoff bounds | Shearer's lemma | information theory | limited independence | Limited independence | Information theory | COMPUTER SCIENCE, SOFTWARE ENGINEERING | MATHEMATICS | MATHEMATICS, APPLIED | ENTROPY | Constrictions | Algorithms | Random variables | Deviation | Mathematical analysis

Chernoff bounds | Shearer's lemma | information theory | limited independence | Limited independence | Information theory | COMPUTER SCIENCE, SOFTWARE ENGINEERING | MATHEMATICS | MATHEMATICS, APPLIED | ENTROPY | Constrictions | Algorithms | Random variables | Deviation | Mathematical analysis

Journal Article

ELECTRONIC COMMUNICATIONS IN PROBABILITY, ISSN 1083-589X, 2019, Volume 24

We give upper and lower asymptotic bounds for the left tail and for the right tail of the continuous limiting QuickSort density f that are nearly matching in each tail...

asymptotic bounds | STATISTICS & PROBABILITY | QuickSort | Landau-Kolmogorov inequality | density tails

asymptotic bounds | STATISTICS & PROBABILITY | QuickSort | Landau-Kolmogorov inequality | density tails

Journal Article

Methodology and computing in applied probability, ISSN 1573-7713, 2018, Volume 21, Issue 2, pp. 461 - 490

In this paper, we compare two numerical methods for approximating the probability that the sum of dependent regularly varying random variables exceeds a high threshold under Archimedean copula models...

Archimedean copulas | Conditional Monte Carlo simulation | Dependent regularly varying random variables | Tail approximation | Numerical bounds | STATISTICS & PROBABILITY | Monte Carlo method | Models | Distribution (Probability theory) | Analysis | Numerical analysis | Approximation | Computer simulation | Dependent variables | Numerical methods | Mathematical models | Probabilistic methods | Random variables | Distribution functions

Archimedean copulas | Conditional Monte Carlo simulation | Dependent regularly varying random variables | Tail approximation | Numerical bounds | STATISTICS & PROBABILITY | Monte Carlo method | Models | Distribution (Probability theory) | Analysis | Numerical analysis | Approximation | Computer simulation | Dependent variables | Numerical methods | Mathematical models | Probabilistic methods | Random variables | Distribution functions

Journal Article

17.
Full Text
A lower bound on the probability that a binomial random variable is exceeding its mean

Statistics and Probability Letters, ISSN 0167-7152, 12/2016, Volume 119, pp. 305 - 309

We provide a lower bound on the probability that a binomial random variable is exceeding its mean...

Binomial tail | Tail conditional expectation | Lower bounds | Hazard rate order | Mean absolute deviation | CONVERGENCE | STATISTICS & PROBABILITY

Binomial tail | Tail conditional expectation | Lower bounds | Hazard rate order | Mean absolute deviation | CONVERGENCE | STATISTICS & PROBABILITY

Journal Article

ELECTRONIC JOURNAL OF PROBABILITY, ISSN 1083-6489, 2019, Volume 24

...) on the right tail of the limiting QuickSort distribution function F and by Fill and Hung (2018) on the right tails of the corresponding density f and of the absolute derivatives of f of each order...

large deviations | Chernoff bounds | QuickSort | moment generating functions | asymptotic bounds | tails of distributions | STATISTICS & PROBABILITY

large deviations | Chernoff bounds | QuickSort | moment generating functions | asymptotic bounds | tails of distributions | STATISTICS & PROBABILITY

Journal Article

Probability in the engineering and informational sciences, ISSN 0269-9648, 04/2011, Volume 25, Issue 2, pp. 171 - 185

A renewal model in risk theory is considered, where $\overline{H}(u,y)$ is the tail of the distribution of the deficit at ruin with initial surplus u and $\overline{F}(y...

DISTRIBUTIONS | PRESERVATION | STATISTICS & PROBABILITY | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | ENGINEERING, INDUSTRIAL | RUIN | Probability | Risk | Actuarial science | Mathematical models | Statistics | Byproducts | Asymptotic properties | Upper bounds | Ladders

DISTRIBUTIONS | PRESERVATION | STATISTICS & PROBABILITY | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | ENGINEERING, INDUSTRIAL | RUIN | Probability | Risk | Actuarial science | Mathematical models | Statistics | Byproducts | Asymptotic properties | Upper bounds | Ladders

Journal Article

Statistics & probability letters, ISSN 0167-7152, 2018, Volume 139, pp. 67 - 74

<1 with probability at least 1∕4 strictly exceeds its expectation. We also show that for 1...

Binomial tail | Lower bounds | STATISTICS & PROBABILITY

Binomial tail | Lower bounds | STATISTICS & PROBABILITY

Journal Article

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