# A central limit theorem for triangular arrays of weakly dependent random variables, with applications in statistics

ESAIM: Probability and Statistics (2013)

- Volume: 17, page 120-134
- ISSN: 1292-8100

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topNeumann, Michael H.. "A central limit theorem for triangular arrays of weakly dependent random variables, with applications in statistics." ESAIM: Probability and Statistics 17 (2013): 120-134. <http://eudml.org/doc/274351>.

@article{Neumann2013,

abstract = {We derive a central limit theorem for triangular arrays of possibly nonstationary random variables satisfying a condition of weak dependence in the sense of Doukhan and Louhichi [Stoch. Proc. Appl. 84 (1999) 313–342]. The proof uses a new variant of the Lindeberg method: the behavior of the partial sums is compared to that of partial sums of dependent Gaussian random variables. We also discuss a few applications in statistics which show that our central limit theorem is tailor-made for statistics of different type.},

author = {Neumann, Michael H.},

journal = {ESAIM: Probability and Statistics},

keywords = {central limit theorem; Lindeberg method; weak dependence; bootstrap; triangular array},

language = {eng},

pages = {120-134},

publisher = {EDP-Sciences},

title = {A central limit theorem for triangular arrays of weakly dependent random variables, with applications in statistics},

url = {http://eudml.org/doc/274351},

volume = {17},

year = {2013},

}

TY - JOUR

AU - Neumann, Michael H.

TI - A central limit theorem for triangular arrays of weakly dependent random variables, with applications in statistics

JO - ESAIM: Probability and Statistics

PY - 2013

PB - EDP-Sciences

VL - 17

SP - 120

EP - 134

AB - We derive a central limit theorem for triangular arrays of possibly nonstationary random variables satisfying a condition of weak dependence in the sense of Doukhan and Louhichi [Stoch. Proc. Appl. 84 (1999) 313–342]. The proof uses a new variant of the Lindeberg method: the behavior of the partial sums is compared to that of partial sums of dependent Gaussian random variables. We also discuss a few applications in statistics which show that our central limit theorem is tailor-made for statistics of different type.

LA - eng

KW - central limit theorem; Lindeberg method; weak dependence; bootstrap; triangular array

UR - http://eudml.org/doc/274351

ER -

## References

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