An introduction to econometric applications of empirical process theory for dependent random variables

1993 ◽  
Vol 12 (2) ◽  
pp. 183-216 ◽  
Author(s):  
Donald Andrews
Keyword(s):  
Empirical Process ◽  
Random Variables ◽  
Process Theory ◽  
Dependent Random Variables ◽  
Empirical Process Theory

scholarly journals General Bootstrap for Dual ϕ-Divergence Estimates

2012 ◽  
Vol 2012 ◽  
pp. 1-33 ◽  
Author(s):  
Salim Bouzebda ◽  
Mohamed Cherfi
Keyword(s):  
Coverage Probability ◽  
Empirical Process ◽  
Asymptotic Properties ◽  
Process Theory ◽  
General Notion ◽  
Finite Sample ◽  
Confidence Set ◽  
Empirical Process Theory ◽  
Divergence Estimates ◽  
Simulation Results

A general notion of bootstrappedϕ-divergence estimates constructed by exchangeably weighting sample is introduced. Asymptotic properties of these generalized bootstrappedϕ-divergence estimates are obtained, by means of the empirical process theory, which are applied to construct the bootstrap confidence set with asymptotically correct coverage probability. Some of practical problems are discussed, including, in particular, the choice of escort parameter, and several examples of divergences are investigated. Simulation results are provided to illustrate the finite sample performance of the proposed estimators.

scholarly journals On Some Conditions for Strong Law of Large Numbers for Weighted Sums of END Random Variables under Sublinear Expectations

2019 ◽  
Vol 2019 ◽  
pp. 1-8
Author(s):  
Xiaochen Ma ◽  
Qunying Wu
Keyword(s):  
Probability Space ◽  
Law Of Large Numbers ◽  
Random Variables ◽  
Weighted Sums ◽  
Dependent Random Variables ◽  
Strong Law ◽  
Sublinear Expectation ◽  
Negatively Dependent Random Variables ◽  
Large Numbers ◽  
End Random Variables

In this article, we research some conditions for strong law of large numbers (SLLNs) for weighted sums of extended negatively dependent (END) random variables under sublinear expectation space. Our consequences contain the Kolmogorov strong law of large numbers and the Marcinkiewicz strong law of large numbers for weighted sums of extended negatively dependent random variables. Furthermore, our results extend strong law of large numbers for some sequences of random variables from the traditional probability space to the sublinear expectation space context.

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