Convergence in mean and central limit theorems for weighted sums of martingale difference random vectors with infinite rth moments

Statistics ◽  
2021 ◽  
pp. 1-23
Author(s):  
L. V. Dung ◽  
T. C. Son ◽  
T. T. Tu
2020 ◽  
Vol 2020 ◽  
pp. 1-9
Author(s):  
Zhicheng Chen ◽  
Xinsheng Liu

Under suitable conditions, the almost sure central limit theorems for the maximum of general standard normal sequences of random vectors are proved. The simulation of the almost sure convergence for the maximum is firstly performed, which helps to visually understand the theorems by applying to two new examples.


2009 ◽  
Vol 25 (3) ◽  
pp. 748-763 ◽  
Author(s):  
Kairat T. Mynbaev

Standardized slowly varying regressors are shown to be Lp-approximable. This fact allows us to provide alternative proofs of asymptotic expansions of nonstochastic quantities and central limit results due to P.C.B. Phillips, under a less stringent assumption on linear processes. The recourse to stochastic calculus related to Brownian motion can be completely dispensed with.


1997 ◽  
Vol 13 (3) ◽  
pp. 353-367 ◽  
Author(s):  
Robert M. de Jong

This paper presents central limit theorems for triangular arrays of mixingale and near-epoch-dependent random variables. The central limit theorem for near-epoch-dependent random variables improves results from the literature in various respects. The approach is to define a suitable Bernstein blocking scheme and apply a martingale difference central limit theorem, which in combination with weak dependence conditions renders the result. The most important application of this central limit theorem is the improvement of the conditions that have to be imposed for asymptotic normality of minimization estimators.


2014 ◽  
Vol 123 (3) ◽  
pp. 305-307 ◽  
Author(s):  
Abdelkamel Alj ◽  
Rajae Azrak ◽  
Guy Mélard

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