Sur un nouveau théorème-limite de la théorie des probabilités

By Harald Cramér. 2018

395 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/7cef96e6625cbdb32e315f62f955f9cfde37051f

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In Statistics and Probability

Citations in the corpus

Time-uniform, nonparametric, nonasymptotic confidence sequences (2018, methodology): “2)), itself based on the classical Cramér-Chernoff method ((Cramér, 1938; Chernoff, 1952); (Boucheron et al.”
Mod-ϕ Convergence (2016, background): “random variables has received some attention in the literature on limit theorems (originally in [Cra38], see also [IL71]).”
Bayesian Gaussian process models : PAC-Bayesian generalisation error bounds and sparse approximations (2003, methodology): “The technique is often accredited to Chernoff [28], but has actually been used by Cramér before [35]: Pr {X ≥ x} = Pr { e ≥ e } ≤ eE [ e ]”
On Large Deviations of Sums of Independent Random Variables (2007, result): “1 that corresponds to the two-sided Cramér’s condition: Ee1 < ∞ for − H < h < H and some H > 0. (1.6) Corollary 1.1 Let X1, X2, · · · be a sequence of i.i.d. random variables satisfying conditions (1.4) and (1.6), and let EX1 = 0, EX 2 1 = 1. If 0 < H ′ < H, then relation (1.5) holds uniformly in x ”
Random Walks on Reductive Groups (2016, background): “The classical Large Deviations Principle is due to Cramér in [35] (see [39] for a modern account of the LDP).”
Time-uniform Chernoff bounds via nonnegative supermartingales (2018, methodology): “The Cramér-Chernoff method takes its name from the works of Cramér (1938) and Chernoff (1952).”
The large deviation approach to statistical mechanics (2008, methodology): “25 The second derivation is based on a clever change of measure which goes back to Cramér [1], and which is commonly used nowadays to prove large deviation principles.”
From Stein identities to moderate deviations (2009, neutral): “Introduction Moderate deviations date back to Cramér (1938) who obtained expansions for tail probabilities for sums of independent random variables about the nor- ∗Partially supported by Grant C-389-000-010-101 at the National University of Singapore †Partially supported by Hong Kong RGC CERG -…”
Moderate Deviations via Cumulants (2010, background): “partial sums the classical result due to Cramér [11] is that if Ee |X1|1/2 <∞ for some t > 0, (1.”
Multifractal rainfall extremes: Theoretical analysis and practical estimation (2009, methodology): “a) is that it can be obtained also from large deviation theory, using Cramer’s refined limit [23, 25-27],.”
Exponential inequalities for martingales and asymptotic properties of the free energy of directed polymers in a random environment (2008, background): “the classical works of Bernstein (1924, [3]), Cramér (1938, [15]), Hoeffding (1963, [22]), Azuma (1967, [1]), Chernoff (1981, [8]), the books of Chow and Teicher (1978, [9]), and Petrov (1995, [31]), and the recent papers by de la Peña, (1999, [16]), Lesigne and Volný (2001, [27]), Bentkus (2004, [2”