Cramer-chernoff
WebDec 1, 2009 · Abstract En este trabajo se desarrolla un teorema de tipo Chernoff para la distan-cia L1 entre estimadores núcleo procedentes de muestras aleatorias indepen-dientes e idénticamente distribuidas. Webfirst estimate of this kind can be traced back to Cramer’s paper [´ 6], which deals with variables possessing a density and exponential moments. In [5] Chernoff relaxed the first assumption. Bahadur [2] finally gave a proof without any assumption on the law of X1. Coming from statistical mechanics, Lanford imported the subadditivity argument
Cramer-chernoff
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Webvariables has been given by Kolmogorov (1929), Cramer (1938), Chernoff (1952), Bahadur and Ranga Rao (1960) and Bennett (1962), but the sam-ples in Markov chains are … WebFixedtime Chernoff 0 x 0 m V t Upper bound on S t Figure 1: Comparison of (i) xed-time Cram er-Cherno bound, which bounds the deviations of S m at a xed time m; (ii) …
WebOct 21, 2024 · The Chernoff-Cramèr bound is a widely used technique to analyze the upper tail bound of random variable based on its moment generating function. By elementary proofs, we develop a user-friendly reverse Chernoff-Cramèr bound that yields non-asymptotic lower tail bounds for generic random variables. The new reverse Chernoff … WebWe derive a simple concentration inequality for the propagation of the input uncertainty through the network using the Cramer-Chernoff method and estimates of the local variation of the neural network mapping computed at the training points. We further discuss and exploit the resulting condition on the network to regularize the loss function ...
WebW Gregory Chernoff 1 , Harvey Cramer, Stephanie Su-Huang. Affiliation 1 Chernoff Plastic Surgery and Laser Center, 830 Second Street, Santa Rosa, CA 95404, USA. [email protected]; PMID: 17700980 DOI: 10.1007/s00266-006-0218-1 … WebIn probability theory, the theory of large deviations concerns the asymptotic behaviour of remote tails of sequences of probability distributions. While some basic ideas of the …
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. the locker room nudgeeIn 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 tickets philadelphia airportWebMay 1, 2024 · We use Cramér-Chernoff type estimates in order to study the Calderón-Zygmund structure of the kernels ∑I∈DaI(ω)ψI(x)ψI(y), and their concentration about the mean, where aI are subgaussian ... tickets philharmonieWebJan 1, 1997 · Exponential bounds for self-normalized sums have been obtained by several authors in the unidimensional case or can be derived from non-uniform Berry-Esséen or … the locker room mark greenWebHere is an explicit proof that a standard Chernoff bound is tight up to constant factors in the exponent for a particular range of the parameters. (In particular, whenever the variables … the locker room lewistonWebFeb 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 … the locker room mondovi wiWebDec 1, 2001 · The application of the Cramér-Chernoff method to derive concentration inequalities for (1.0.3) in the context of Markov processes is well established, and this work is based on [47], [35], [12 ... the locker room of montgomery inc