A local maximal inequality under uniform entropy.
نویسندگان
چکیده
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.
منابع مشابه
Empirical spectral processes for locally stationary time series
A time-varying empirical spectral process indexed by classes of functions is defined for locally stationary time series. We derive weak convergence in a function space, and prove a maximal exponential inequality and a Glivenko–Cantelli-type convergence result. The results use conditions based on the metric entropy of the index class. In contrast to related earlier work, no Gaussian assumption i...
متن کاملUniform Ergodic Theorems for Dynamical Systems Under VC Entropy Conditions
The classic limit theorems of Vapnik and Chervonenkis [27,28] show that if a function class F satisfies a random entropy condition, then the strong law of large numbers holds uniformly over F . In this paper we show that an analogous weighted entropy condition implies that Birkhoff’s pointwise ergodic theorem holds uniformly over F . In this way we obtain a variety of uniform ergodic theorems f...
متن کاملHeat, temperature and Clausius inequality in a model for active Brownian particles
Methods of stochastic thermodynamics and hydrodynamics are applied to a recently introduced model of active particles. The model consists of an overdamped particle subject to Gaussian coloured noise. Inspired by stochastic thermodynamics, we derive from the system's Fokker-Planck equation the average exchanges of heat and work with the active bath and the associated entropy production. We show ...
متن کاملThe Uniform Ergodic Theorem for Dynamical Systems
Necessary and sufficient conditions are given for the uniform convergence over an arbitrary index set in von Neumann’s mean and Birkhoff’s pointwise ergodic theorem. Three different types of conditions already known from probability theory are investigated. Firstly it is shown that the property of being eventually totally bounded in the mean is necessary and sufficient. This condition involves ...
متن کاملMaximal violation of Bell inequalities under local filtering
We investigate the behavior of the maximal violations of the CHSH inequality and Vèrtesi's inequality under the local filtering operations. An analytical method has been presented for general two-qubit systems to compute the maximal violation of the CHSH inequality and the lower bound of the maximal violation of Vértesi's inequality over the local filtering operations. We show by examples that ...
متن کاملذخیره 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 ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Electronic journal of statistics
دوره 5 2011 شماره
صفحات -
تاریخ انتشار 2011