amount. Hoeffding's inequality was proven by Wassily Hoeffding in 1963. Hoeffding's inequality is a special case of the Azuma–Hoeffding inequality and McDiarmid's...

statistics, in which Hoeffding contributed the idea and basic results on U-statistics. In probability theory, Hoeffding's inequality provides an upper bound...

Bernstein inequalities are also known as the Chernoff bound, Hoeffding's inequality and Azuma's inequality. The martingale case of the Bernstein inequality is...

Markov's inequality or Chebyshev's inequality. The Chernoff bound is related to the Bernstein inequalities. It is also used to prove Hoeffding's inequality, Bennett's...

inequality - a summary of tail-bounds on random variables. It is not a direct application of Hoeffding's lemma though. The statement of Hoeffding's lemma...

Cramér–Rao inequality Hoeffding's inequality Hölder's inequality Inequality of arithmetic and geometric means Jensen's inequality Kolmogorov's inequality Markov's...

between the sum and its expected value. Several inequalities can be used. 1. Hoeffding's inequality says that: Pr [ | S n − E n | > t ] ≤ 2 exp ⁡ ( −...

inequality, relies on symmetrization, and then argue conditionally on the data using concentration inequalities (in particular Hoeffding's inequality)...

mathematical statistician Wassily Hoeffding. The proof of Hoeffding's lemma uses Taylor's theorem and Jensen's inequality. Hoeffding's lemma is itself used in the...

X\Vert _{\mathrm {vp} }^{2}\leq \left({\frac {b-a}{2}}\right)^{2}} . Hoeffding's inequality is the Chernoff bound obtained using this fact. Since the sum of...

inequality and its improvement, respectively. Hoeffding's inequality only assumes the summands are bounded almost surely, while Bennett's inequality offers...

correlation inequality Gaussian isoperimetric inequality Gibbs's inequality Hoeffding's inequality Hoeffding's lemma Jensen's inequality Khintchine inequality Kolmogorov's...

1 } {\displaystyle f:{\mathcal {X}}\to \{0,1\}} . We can apply Hoeffding's inequality to bound the probability that the empirical risk deviates from the...

Hodges' estimator Hodges–Lehmann estimator Hoeffding's independence test Hoeffding's lemma Hoeffding's inequality Holm–Bonferroni method Holtsmark distribution...

upper tail of the cumulative distribution function for k ≥ np. Hoeffding's inequality yields the simple bound F ( k ; n , p ) ≤ exp ⁡ ( − 2 n ( p − k...

summands in Matrix Azuma are independent gives a matrix extension of Hoeffding's inequalities. Consider a finite sequence { X k } {\displaystyle \{\mathbf {X}...

(1889–1982), surgeon Wassily Hoeffding (1914–1991), statistician who introduced U-statistic and known for Hoeffding's inequality Julius Hoffory (1855-1897)...

P(S_{n}\geq x)\leq e^{-x^{2}/2}} This last bound is related to the Hoeffding's inequality. In the uniform case where all the bi = n−1/2 the maximum value...

2 k ) {\displaystyle O(n^{2k})} and take the majority vote. By Hoeffding's inequality, this gives us a BPP algorithm. The important thing is that this...

y)} . For a fixed ( x , y ) {\displaystyle (x,y)} , we can use Hoeffding's inequality to get the following equation: Pr R [ | p R ′ ( x , y ) − p ( x...

{\displaystyle \beta _{i}} and both the possibilities are equally likely. By Hoeffding's inequality, this is at most 2 e − m ε 2 / 8 {\displaystyle 2e^{-m\varepsilon...

Markov's inequality Chebyshev's inequality = Chernoff bound Chernoff's inequality Bernstein inequalities (probability theory) Hoeffding's inequality Kolmogorov's...

concentrated around its expected value. In particular, from the Azuma–Hoeffding inequality, they prove that Pr ( | q − E [ q ] | ≥ λ m ) ≤ 2 exp ⁡ ( − 2 λ 2...

The binomial sum variance inequality states that the variance of the sum of binomially distributed random variables will always be less than or equal to...

power inequality Etemadi's inequality / (F:R) Gauss's inequality Hoeffding's inequality / (F:R) Khintchine inequality / (F:B) Kolmogorov's inequality / (F:R)...

formulae involves the analysis of recursive functions and the Azuma-Hoeffding Inequality. It is observable that for l = 1 {\displaystyle l=1} and p = 0 {\displaystyle...

factor of 1+a of the exact value. Various lemmas, such as Hoeffding's lemma or Bennett's inequality provide bounds on the moment-generating function in the...

covariance between two random variables X , Y {\displaystyle X,Y} is the Hoeffding's covariance identity: cov ⁡ ( X , Y ) = ∫ R ∫ R ( F ( X , Y ) ( x , y...

theory, particularly the theory of martingales. The Burkholder–Davis–Gundy inequality is co-named after him. Burkholder spent most of his professional career...

Note that this result generalizes the rearrangement inequality and Chebyshev's sum inequality. Copula (probability theory) (X*, Y*) always exists, take...