Sharpening jensen's inequality
WebbThe inequality (1.5)is appropriate for iteration, using a sequence of functions. e. 1, e. 2, e. 3, ..., as in the case of Bessel’s inequality, but if. c. θ,r < 1 there is an exponential decay of the coefficients in the analogue of Bessel’s inequality. We note that the inequality (1.5)holds trivially for. c. θ,r =0by Hölder’s inequality ... WebbThis article proposes a new sharpened version of Jensen's inequality. The proposed new bound is simple and insightful, is broadly applicable by imposing minimum assumptions, …
Sharpening jensen's inequality
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Webb琴生不等式 （英語： Jensen's inequality ，台湾稱作 簡森不等式 [1] ），或稱 延森不等式 ，以 丹麥 數學家 約翰·延森 命名。 它給出 積分 的 凸函數 值和凸函數的積分值間的關係，在此不等式最簡單形式中，闡明了對一平均做凸函數轉換，會小於等於先做凸函數轉換再平均。 若將簡森不等式應用在二點上，就回到了 凸函數 的基本性質：过一个凸函数上任意 … In mathematics, Jensen's inequality, named after the Danish mathematician Johan Jensen, relates the value of a convex function of an integral to the integral of the convex function. It was proved by Jensen in 1906, building on an earlier proof of the same inequality for doubly-differentiable functions by Otto Hölder … Visa mer The classical form of Jensen's inequality involves several numbers and weights. The inequality can be stated quite generally using either the language of measure theory or (equivalently) probability. In the … Visa mer Form involving a probability density function Suppose Ω is a measurable subset of the real line and f(x) is a non-negative function such that $${\displaystyle \int _{-\infty }^{\infty }f(x)\,dx=1.}$$ Visa mer • Jensen's Operator Inequality of Hansen and Pedersen. • "Jensen inequality", Encyclopedia of Mathematics, EMS Press, 2001 [1994] • Weisstein, Eric W. "Jensen's inequality". MathWorld. Visa mer Jensen's inequality can be proved in several ways, and three different proofs corresponding to the different statements above will be offered. Before embarking on these … Visa mer • Karamata's inequality for a more general inequality • Popoviciu's inequality • Law of averages • A proof without words of Jensen's inequality Visa mer
WebbHowever, applying Jensen on log-sums in Ie and £(XIE» is not as straightforward. Some terms in these expressions involve negative log-sums and so Jensen is actually solving for an upper bound on those terms. If we want overall lower and upper bounds on Ie and £(XIE», we need to compute reverse-Jensen bounds. 5 Reverse-Jensen Bounds Webb1 sep. 2024 · This post is all about Jensen’s inequality, an elementary but powerful result about convex functions. It comes up all over the place in mathematics, probably because the concept of convexity is itself so fundamental. I ran into it recently as I was thinking about relative entropy and why it is so well behaved; I think a lot of it comes down to the …
WebbIn this article, we consider the generalized forms of the Jensen's inequality given by Jessen and McShane for isotonic linear functionals, derive several refinements for the Jessen's and McShane's inequalities connected to certain functions from the linear space, generalize the Jessen's and McShane's inequalities pertaining n certain functions. WebbJensen’s inequality is covered in all major statistical textbooks such as Casella and Berger ( 2002, Section 4.7) and Wasserman ( 2013, Section 4.2) as a basic mathematical tool …
WebbJensen’s inequality is covered in all major statistical textbooks such as Casella and Berger ( 2002, Section 4.7) and Wasserman ( 2013, Section 4.2) as a basic mathematical tool for statistics. Let X be a random variable with finite expectation and let φ(x) be a convex function. Jensen’s inequality (Jensen, 1906) establishes: E[φ(X)]− φ(E[X]) ≥ 0.
Webb1 Answer. Yes Jensen inequality holds for multiple variable. We can find a general formulation in the mesure theoretic article in Wikipedia. "Let (Ω, A, μ) be a measure space, such that μ (Ω) = 1. If g is a real-valued function that is μ-integrable, and if g is a convex function on the real line. This generalizable for convex function on ... truth social teamWebb28 apr. 2024 · Tour Start here for a quick overview of the site Help Center Detailed answers to any questions you might have Meta Discuss the workings and policies of this site philips induction hobWebbSharpening Jensen's Inequality Published in: The American Statistician, June 2024 DOI: 10.1080/00031305.2024.1419145: Authors: J. G. Liao, Arthur Berg View on publisher site Alert me about new mentions. Twitter Demographics. The data shown below were collected from the profiles of 4 tweeters who shared this research output. philips induction priceWebb10 dec. 2024 · The main aim of this paper is to give an improvement of the recent result on the sharpness of the Jensen inequality. The results given here are obtained using different Green functions and considering the case of the real Stieltjes measure, not necessarily positive. Finally, some applications involving various types of f-divergences and … philips induction stoveWebbDive into the research topics of 'Sharpening Jensen's Inequality'. Together they form a unique fingerprint. Sort by Weight Alphabetically Mathematics. Jensen's inequality 74%. Power Mean 38%. Moment generating function 34%. Presentation 24%. Calculus 23%. Form 12%. Business & Economics. Jensen's Inequality 100%. Moment ... philips industries inc windowsWebbThe main aim of this paper is to give an improvement of the recent result on the sharpness of the Jensen inequality. The results given here are obtained using different Green functions and considering the case of the real Stieltjes measure, not necessarily positive. philips industries batamWebb21 juli 2024 · And I carefully reviewed proof process of Jensen's Inequality and found Why "Jensen's inequality Do Not hold in general finite measure space". I write this thought down for anyone who has the same confusion. In the original Proof: Proof: truth social symbol