Empirical Process Techniques for Dependent Data

2002 ◽  
pp. 3-113 ◽  
Author(s):  
Herold Dehling ◽  
Walter Philipp
Keyword(s):  
Empirical Process ◽  
Dependent Data

scholarly journals Consistency of Hill's estimator for dependent data

1995 ◽  
Vol 32 (01) ◽  
pp. 139-167 ◽  
Author(s):  
Sidney Resnick ◽  
Cătălin Stărică
Keyword(s):  
Infinite Order ◽  
Empirical Process ◽  
Marginal Distribution ◽  
Random Variables ◽  
Ar Model ◽  
Independent Random Variables ◽  
Dependent Data ◽  
Mixing Conditions ◽  
Hill’S Estimator ◽  
Tail Empirical Process

Consider a sequence of possibly dependent random variables having the same marginal distribution F, whose tail 1−F is regularly varying at infinity with an unknown index − α < 0 which is to be estimated. For i.i.d. data or for dependent sequences with the same marginal satisfying mixing conditions, it is well known that Hill's estimator is consistent for α−1 and asymptotically normally distributed. The purpose of this paper is to emphasize the central role played by the tail empirical process for the problem of consistency. This approach allows us to easily prove Hill's estimator is consistent for infinite order moving averages of independent random variables. Our method also suffices to prove that, for the case of an AR model, the unknown index can be estimated using the residuals generated by the estimation of the autoregressive parameters.

scholarly journals Consistency of Hill's estimator for dependent data

1995 ◽  
Vol 32 (1) ◽  
pp. 139-167 ◽  
Author(s):  
Sidney Resnick ◽  
Cătălin Stărică
Keyword(s):  
Infinite Order ◽  
Empirical Process ◽  
Marginal Distribution ◽  
Random Variables ◽  
Ar Model ◽  
Independent Random Variables ◽  
Dependent Data ◽  
Mixing Conditions ◽  
Hill’S Estimator ◽  
Tail Empirical Process

Consider a sequence of possibly dependent random variables having the same marginal distribution F, whose tail 1−F is regularly varying at infinity with an unknown index − α < 0 which is to be estimated. For i.i.d. data or for dependent sequences with the same marginal satisfying mixing conditions, it is well known that Hill's estimator is consistent for α−1 and asymptotically normally distributed. The purpose of this paper is to emphasize the central role played by the tail empirical process for the problem of consistency. This approach allows us to easily prove Hill's estimator is consistent for infinite order moving averages of independent random variables. Our method also suffices to prove that, for the case of an AR model, the unknown index can be estimated using the residuals generated by the estimation of the autoregressive parameters.

scholarly journals Stochastic Equicontinuity for Unbounded Dependent Heterogeneous Arrays

1996 ◽  
Vol 12 (2) ◽  
pp. 347-359 ◽  
Author(s):  
Bruce E. Hansen
Keyword(s):  
Empirical Process ◽  
Dependent Data ◽  
Strong Mixing ◽  
Martingale Difference ◽  
Lipschitz Continuous ◽  
Empirical Process Theory ◽  
Dependence Conditions ◽  
Bounded Functions ◽  
Parametric Functions ◽  
Stochastic Equicontinuity

This paper establishes stochastic equicontinuity for classes of mixingales. Attention is restricted to Lipschitz-continuous parametric functions. Unlike some other empirical process theory for dependent data, our results do not require bounded functions, stationary processes, or restrictive dependence conditions. Applications are given to martingale difference arrays, strong mixing arrays, and near-epoch dependent arrays.

Fundamental Research into Thin Films in a Developing Country

1972 ◽  
Vol 30 ◽  
pp. 500-501
Author(s):  
J.A. Eades ◽  
E. Grünbaum
Keyword(s):  
Thin Films ◽  
Growth Process ◽  
Empirical Process ◽  
Nucleation And Growth ◽  
Research Groups ◽  
Film Research ◽  
Fundamental Research ◽  
Controlled Deposition ◽  
The One ◽  
The University

In the last decade and a half, thin film research, particularly research into problems associated with epitaxy, has developed from a simple empirical process of determining the conditions for epitaxy into a complex analytical and experimental study of the nucleation and growth process on the one hand and a technology of very great importance on the other. During this period the thin films group of the University of Chile has studied the epitaxy of metals on metal and insulating substrates. The development of the group, one of the first research groups in physics to be established in the country, has parallelled the increasing complexity of the field.The elaborate techniques and equipment now needed for research into thin films may be illustrated by considering the plant and facilities of this group as characteristic of a good system for the controlled deposition and study of thin films.

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