Time-uniform Chernoff bounds via nonnegative supermartingales
From MaRDI portal
Publication:2188432
DOI10.1214/18-PS321zbMath1456.60054arXiv1808.03204OpenAlexW3028378217MaRDI QIDQ2188432
Aaditya Ramdas, Steven R. Howard, Jon D. McAuliffe, Jasjeet Sekhon
Publication date: 11 June 2020
Published in: Probability Surveys (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1808.03204
Inequalities; stochastic orderings (60E15) Random matrices (probabilistic aspects) (60B20) Large deviations (60F10) Sample path properties (60G17) Random matrices (algebraic aspects) (15B52)
Related Items
Sequential estimation of quantiles with applications to A/B testing and best-arm identification, Universal inference, Unnamed Item, Game-theoretic statistics and safe anytime-valid inference, Catoni-style confidence sequences for heavy-tailed mean estimation, A composite generalization of Ville's martingale theorem using e-processes, Optional stopping with Bayes factors: a categorization and extension of folklore results, with an application to invariant situations, Sequential testing for elicitable functionals via supermartingales, Interactive martingale tests for the global null, Unnamed Item, Time-uniform, nonparametric, nonasymptotic confidence sequences, Testing exchangeability: fork-convexity, supermartingales and e-processes, On the Bias, Risk, and Consistency of Sample Means in Multi-armed Bandits
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Hoeffding's inequality for supermartingales
- Concentration inequalities and moment bounds for sample covariance operators
- The spectrum of random \(k\)-lifts of large graphs (with possibly large \(k)\)
- Sums of random Hermitian matrices and an inequality by Rudelson
- Freedman's inequality for matrix martingales
- Concentration inequalities for matrix martingales in continuous time
- User-friendly tail bounds for sums of random matrices
- Exponential inequalities for self-normalized martingales with applications
- Pseudo-maximization and self-normalized processes
- \(L_p\)-version of the Dubins-Savage inequality and some exponential inequalities
- Exponential inequalities for sums of weakly dependent variables
- Large deviations techniques and applications.
- Theory and applications of multivariate self-normalized processes
- Sequential analysis. Tests and confidence intervals
- On the amount of variance needed to escape from a strip
- On tail probabilities for martingales
- Random vectors in the isotropic position
- Sharp uniform convexity and smoothness inequalities for trace norms
- Self-normalized large deviations
- A general class of exponential inequalities for martingales and ratios
- Self-normalized processes: exponential inequalities, moment bounds and iterated logarithm laws.
- Optimum bounds for the distributions of martingales in Banach spaces
- Exponential inequalities for martingales, with application to maximum likelihood estimation for counting processes
- Limit distributions of self-normalized sums
- On some extensions of Bernstein's inequality for self-adjoint operators
- Matrix concentration inequalities via the method of exchangeable pairs
- Exponential inequalities for martingales with applications
- Weighted sums of certain dependent random variables
- Convex trace functions and the Wigner-Yanase-Dyson conjecture
- Concentration of Measure Inequalities in Information Theory, Communications, and Coding
- On Generalizations of Tchebychef's Inequality
- An Extremal Problem in Probability Theory
- Probability Inequalities for the Sum of Independent Random Variables
- Concentration Inequalities and Martingale Inequalities: A Survey
- Self-Normalized Processes
- Inequalities for a Pair of Processes Stopped at a Random Time
- Strong converse for identification via quantum channels
- High-Dimensional Statistics
- On the Tchebychef Inequality of Bernstein
- Concentration Inequalities for Sums and Martingales
- Probability Inequalities for Sums of Bounded Random Variables
- A TCHEBYCHEFF-LIKE INEQUALITY FOR STOCHASTIC PROCESSES
- Expansion properties of random Cayley graphs and vertex transitive graphs via matrix martingales
- An Introduction to Matrix Concentration Inequalities
- ITERATED LOGARITHM INEQUALITIES
- Student's t-Test Under Symmetry Conditions
- Convex Analysis
- Statistical Methods Related to the Law of the Iterated Logarithm
- Boundary Crossing Probabilities for the Wiener Process and Sample Sums
- Regularity Properties of Certain Families of Chance Variables
- A Measure of Asymptotic Efficiency for Tests of a Hypothesis Based on the sum of Observations
- Sequential Tests of Statistical Hypotheses
