scholarly journals Almost sure central limit theorems for m-dependent random variables

Filomat ◽  
2017 ◽  
Vol 31 (18) ◽  
pp. 5581-5590 ◽  
Author(s):  
Yu Miao ◽  
Xiaoyan Xu
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
Limit Theorems ◽  
Random Sequence ◽  
Random Variables ◽  
Dependent Random Variables ◽  
Moment Conditions ◽  
Dependent Sequence ◽  
The Moment

In the present paper, the almost sure central limit theorem for them-dependent random sequence is established, which weakens the moment conditions of Giuliano [10] for the stationary m-dependent sequence and gets the same results with different methods.

Central Limit Theorems for Dependent Heterogeneous Random Variables

1997 ◽  
Vol 13 (3) ◽  
pp. 353-367 ◽  
Author(s):  
Robert M. de Jong
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
Limit Theorems ◽  
Random Variables ◽  
Central Limit Theorems ◽  
Martingale Difference ◽  
Dependent Random Variables ◽  
The Central Limit Theorem ◽  
Dependence Conditions

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.

A central limit theorem by remainder term for renewal processes

1992 ◽  
Vol 24 (2) ◽  
pp. 267-287 ◽  
Author(s):  
Allen L. Roginsky
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
Remainder Term ◽  
Limit Theorems ◽  
Random Variables ◽  
Central Limit Theorems ◽  
Renewal Processes

Three different definitions of the renewal processes are considered. For each of them, a central limit theorem with a remainder term is proved. The random variables that form the renewal processes are independent but not necessarily identically distributed and do not have to be positive. The results obtained in this paper improve and extend the central limit theorems obtained by Ahmad (1981) and Niculescu and Omey (1985).

A Central Limit Theorem for Cumulative Processes

1994 ◽  
Vol 26 (01) ◽  
pp. 104-121 ◽  
Author(s):  
Allen L. Roginsky
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Rate Of Convergence ◽  
Central Limit ◽  
Remainder Term ◽  
Limit Theorems ◽  
Random Variables ◽  
Central Limit Theorems ◽  
Independent Random Variables ◽  
Cumulative Processes

A central limit theorem for cumulative processes was first derived by Smith (1955). No remainder term was given. We use a different approach to obtain such a term here. The rate of convergence is the same as that in the central limit theorems for sequences of independent random variables.

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