Webimsart-generic ver. 2012/08/31 file: Chernoff-Cramer.tex date: October 5, 2024. Wellner/Cram er - Cherno 4 Taking expectations across the inequality in the last display … WebApr 20, 2024 · In the first part the extended Perron–Frobenius theorem is used to obtain a large deviation theorem of the Cramér–Chernoff type for a class of Markov processes. In the second part the large deviation framework is extended to large deviations for the empirical distributions of a class of Markov processes originally obtained by Donsker and ...
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WebFeb 10, 2024 · Chernoff-Cramer bound The Chernoff-Cramèr inequality is a very general and powerful way of bounding random variables . Compared with the famous Chebyshev … WebTime-uniform Chernoff bounds via nonnegative supermartingales. S. R. Howard, A. Ramdas, J. McAuliffe, J. Sekhon. Probability Surveys, 2024. We give a powerful, general formulation of the Cramér-Chernoff method …
WebFrom (1), the Cramer-Chernoff method (´ Boucheron et al., 2013) derives Hoeffding’s in-equality as follows. For any >0, P Xn i=1 Z i n i=1 EZ i > ! exp 2 2 P n i=1 (b i a i)2/4 . (2) Similar bounds apply to the lower deviation P n i=1 Z i P n i=1 EZ i < as well as the two-sided deviation P n i=1 Z i P n i=1 EZ i > , with an additional ... WebJan 19, 2024 · Please join the Simons Foundation and our generous member organizations in supporting arXiv during our giving campaign September 23-27. 100% of your contribution will fund improvements and new initiatives to benefit arXiv's global scientific community.
WebJul 14, 2016 · Azencott, R. (1980) Grandes déviations: théorèmes à la Cramer-Chernoff et petites perturbations de systèmes dynamiques. Ecole d'Eté de Probabilités de Saint-Flour VIII, 1978. Lecture Notes in Mathematiques 774, Springer-Verlag, Berlin.Google Scholar. Barra, J. R. (1971) Notions fondamentales de statistique mathématique.
In probability theory, a Chernoff bound is an exponentially decreasing upper bound on the tail of a random variable based on its moment generating function or exponential moments. The minimum of all such exponential bounds forms the Chernoff or Chernoff-Cramér bound, which may decay … See more The generic Chernoff bound for a random variable $${\displaystyle X}$$ is attained by applying Markov's inequality to $${\displaystyle e^{tX}}$$ (which is why it sometimes called the exponential Markov or exponential … See more The bounds in the following sections for Bernoulli random variables are derived by using that, for a Bernoulli random variable $${\displaystyle X_{i}}$$ with probability p of being equal to 1, One can encounter … See more Rudolf Ahlswede and Andreas Winter introduced a Chernoff bound for matrix-valued random variables. The following version of the inequality can be found in the work of Tropp. Let M1, ..., Mt be independent matrix valued random … See more When X is the sum of n independent random variables X1, ..., Xn, the moment generating function of X is the product of the individual moment generating functions, giving that: See more Chernoff bounds may also be applied to general sums of independent, bounded random variables, regardless of their distribution; this is known as Hoeffding's inequality. The proof follows a similar approach to the other Chernoff bounds, but applying See more Chernoff bounds have very useful applications in set balancing and packet routing in sparse networks. The set balancing problem arises while designing statistical experiments. Typically while designing a statistical experiment, given the features … See more The following variant of Chernoff's bound can be used to bound the probability that a majority in a population will become a minority in a sample, or vice versa. Suppose there is a general population A and a sub-population B ⊆ A. Mark the relative size of the … See more
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