scholarly journals An Empirical Process Central Limit Theorem for Multidimensional Dependent Data

2012 ◽  
Vol 27 (1) ◽  
pp. 249-277 ◽  
Author(s):  
Olivier Durieu ◽  
Marco Tusche
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
Empirical Process ◽  
Dependent Data

A Central Limit Theorem in Non-parametric Regression with Truncated, Censored and Dependent Data

2014 ◽  
Vol 42 (1) ◽  
pp. 256-269 ◽  
Author(s):  
Han-Ying Liang ◽  
Jacobo de Uña-álvarez ◽  
María del carmen Iglesias-pérez
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
Dependent Data ◽  
Parametric Regression ◽  
Non Parametric

EMPIRICAL INVARIANCE PRINCIPLE FOR ERGODIC TORUS AUTOMORPHISMS: GENERICITY

2008 ◽  
Vol 08 (02) ◽  
pp. 173-195 ◽  
Author(s):  
OLIVIER DURIEU ◽  
PHILIPPE JOUAN
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
Invariance Principle ◽  
Morse Function ◽  
Empirical Process ◽  
Stationary Process ◽  
Sufficient Condition ◽  
Hölder Continuous ◽  
Morse Functions

We consider the dynamical system given by an algebraic ergodic automorphism T on a torus. We study a Central Limit Theorem for the empirical process associated to the stationary process (f◦Ti)i∈ℕ, where f is a given ℝ-valued function. We give a sufficient condition on f for this Central Limit Theorem to hold. In the second part, we prove that the distribution function of a Morse function is continuously differentiable if the dimension of the manifold is at least three and Hölder continuous if the dimension is one or two. As a consequence, the Morse functions satisfy the empirical invariance principle, which is therefore generically verified.

scholarly journals An empirical almost sure central limit theorem under the weak dependence assumptions and its application to copula processes

2017 ◽  
Vol 71 (1) ◽  
pp. 11
Author(s):  
Marcin Dudziński
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
Empirical Process ◽  
Weak Dependence ◽  
Dependence Conditions

Let: \(\mathbf{Y=}\left( \mathbf{Y}_{i}\right)\), where \(\mathbf{Y}_{i}=\left( Y_{i,1},...,Y_{i,d}\right)\), \(i=1,2,\dots \), be a \(d\)-dimensional, identically distributed, stationary, centered process with uniform marginals and a joint cdf \(F\), and \(F_{n}\left( \mathbf{x}\right) :=\frac{1}{n}\sum_{i=1}^{n}\mathbb{I}\left(Y_{i,1}\leq x_{1},\dots ,Y_{i,d}\leq x_{d}\right)\) denote the corresponding empirical cdf. In our work, we prove the almost sure central limit theorem for an empirical process \(B_{n}=\sqrt{n}\left( F_{n}-F\right)\) under some weak dependence conditions due to Doukhan and Louhichi. Some application of the established result to copula processes is also presented.

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