Nettet霍夫丁不等式适用于有界的随机变量，设两两独立的随机变量 X_1,X_2,\cdots,X_n ,假设对所有的 X_i 都是有界的变量，即满足： P (X_i\in [a_i,b_i])=1\\ 那么 n 个随机变量的经验期望（均值）： \bar {X}=\frac {X_1+X_1+\cdots+X_n} {n}\\ 满足以下不等式： Nettet霍夫丁不等式适用于有界的随机变量，设两两独立的随机变量 X_1,X_2,\cdots,X_n ,假设对所有的 X_i 都是有界的变量，即满足： P (X_i\in [a_i,b_i])=1\\ 那么 n 个随机变量的经 …
Hoeffding
In probability theory, Hoeffding's inequality provides an upper bound on the probability that the sum of bounded independent random variables deviates from its expected value by more than a certain amount. Hoeffding's inequality was proven by Wassily Hoeffding in 1963. Hoeffding's inequality is a … Se mer Let X1, ..., Xn be independent random variables such that $${\displaystyle a_{i}\leq X_{i}\leq b_{i}}$$ almost surely. Consider the sum of these random variables, $${\displaystyle S_{n}=X_{1}+\cdots +X_{n}.}$$ Se mer The proof of Hoeffding's inequality follows similarly to concentration inequalities like Chernoff bounds. The main difference is the use of Hoeffding's Lemma: Suppose X is a real … Se mer • Concentration inequality – a summary of tail-bounds on random variables. • Hoeffding's lemma Se mer The proof of Hoeffding's inequality can be generalized to any sub-Gaussian distribution. In fact, the main lemma used in the proof, Hoeffding's lemma, implies that bounded random variables are sub-Gaussian. A random variable X is called sub-Gaussian, if Se mer Confidence intervals Hoeffding's inequality can be used to derive confidence intervals. We consider a coin that shows heads with probability p and tails with … Se mer NettetHarald Høffding (11 March 1843 – 2 July 1931) was a Danish philosopher and theologian . Life [ edit] Born and educated in Copenhagen, he became a schoolmaster, and ultimately in 1883 a professor at the University of … show lights remote control model al69tx
Hoeffding 不等式（霍夫丁不等式）简介 - 刘冲的博客
Nettet7. mar. 2024 · In probability theory, Hoeffding's lemma is an inequality that bounds the moment-generating function of any bounded random variable. [1] It is named after the Finnish– United States mathematical statistician Wassily Hoeffding . The proof of Hoeffding's lemma uses Taylor's theorem and Jensen's inequality. Nettet霍夫丁不等式 （英語： Hoeffding's inequality ）适用于有界的随机变量。 设有两两独立的一系列随机变量 。 假设对所有的 ， 都是 几乎 有界的变量，即满足： 那么这n个随机 … Nettet8. mai 2024 · 霍夫丁不等式适用于有界的随机变量。 设有两两独立的一系列随机变量 X1, …, Xn 。 假设对所有的 Xi 都是几乎有界（看成有界就好了）的变量，即满足： P(Xi ∈ … show lights png