An Upper Bound for Uniform Entropy Numbers

نویسندگان

  • Jon A. Wellner
  • Shuguang Song
چکیده

Let r > 1 and let Q be a probability measure on a measurable space (X, .4). In this note, we present a proof of a useful bound in Lr ( Q)-norm for the entropy of a convex hull in the case that covering numbers for a class of measurable functions are polynomial.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Numerical Investigation of Nanofluid Mixed Convection and Entropy Generation in an Inclined Ventilating Cavity

This paper presents results of a numerical study of mixed convection and entropy generation of Cu–water nanofluid in a square ventilating cavity at different inclination angles. Except a piece of bottom wall with a uniform heat flux, all of the cavity walls are insulated. The inlet port is placed at the bottom of the left wall and the outlet port is positioned at the top of the right wall....

متن کامل

On trees attaining an upper bound on the total domination number

‎A total dominating set of a graph $G$ is a set $D$ of vertices of $G$ such that every vertex of $G$ has a neighbor in $D$‎. ‎The total domination number of a graph $G$‎, ‎denoted by $gamma_t(G)$‎, ‎is~the minimum cardinality of a total dominating set of $G$‎. ‎Chellali and Haynes [Total and paired-domination numbers of a tree, AKCE International ournal of Graphs and Combinatorics 1 (2004)‎, ‎6...

متن کامل

A local maximal inequality under uniform entropy.

We derive an upper bound for the mean of the supremum of the empirical process indexed by a class of functions that are known to have variance bounded by a small constant δ. The bound is expressed in the uniform entropy integral of the class at δ. The bound yields a rate of convergence of minimum contrast estimators when applied to the modulus of continuity of the contrast functions.

متن کامل

The Rate of Rényi Entropy for Irreducible Markov Chains

In this paper, we obtain the Rényi entropy rate for irreducible-aperiodic Markov chains with countable state space, using the theory of countable nonnegative matrices. We also obtain the bound for the rate of Rényi entropy of an irreducible Markov chain. Finally, we show that the bound for the Rényi entropy rate is the Shannon entropy rate.

متن کامل

Quantum Collision-Resistance of Non-uniformly Distributed Functions: Upper and Lower Bounds

We study the quantum query complexity of finding a collision for a function f whose outputs are chosen according to a non-uniform distribution D. We derive some upper bounds and lower bounds depending on the min-entropy and the collision-entropy of D. In particular, we improve the previous lower bound in [TTU16] from Ω(2) to Ω(2) where k is the min-entropy of D.

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2002