### Abstract

Original language | English |
---|---|

Pages (from-to) | 141-147 |

Number of pages | 7 |

Journal | Statistics and Probability Letters |

Volume | 83 |

Issue number | 1 |

Early online date | 23 Aug 2012 |

DOIs | |

Publication status | Published - Jan 2013 |

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### Keywords

- Variance extimation
- Weakly dependent Processes
- Subsampling techniques
- Central limit theorem
- Functionals of mixing processes

### Cite this

*Statistics and Probability Letters*,

*83*(1), 141-147. https://doi.org/10.1016/j.spl.2012.08.012

**Estimation of the Variance of Partial Sums of Dependent Processes.** / Vogel, Daniel; Dehling, Herold; Fried, Roland ; Sharipov, Olimjon; Wornowizki, Max.

Research output: Contribution to journal › Article

*Statistics and Probability Letters*, vol. 83, no. 1, pp. 141-147. https://doi.org/10.1016/j.spl.2012.08.012

}

TY - JOUR

T1 - Estimation of the Variance of Partial Sums of Dependent Processes

AU - Vogel, Daniel

AU - Dehling, Herold

AU - Fried, Roland

AU - Sharipov, Olimjon

AU - Wornowizki, Max

N1 - The authors were supported in part by the Collaborative Research Grant 823, Project C3 Analysis of Structural Change in Dynamic Processes, of the German Research Foundation.

PY - 2013/1

Y1 - 2013/1

N2 - We study subsampling estimators for the limit variance σ2=V ar(X1)+2∑∞k=2Cov(X1,Xk) of partial sums of a stationary stochastic process (Xk)k≥1. We establish L2-consistency of a non-overlapping block resampling method. Our results apply to processes that can be represented as functionals of strongly mixing processes. Motivated by recent applications to rank tests, we also study estimators for the series V ar(F(X1))+2∑∞k=2Cov(F(X1),F(Xk)), where F is the distribution function of X1. Simulations illustrate the usefulness of the proposed estimators and of a mean squared error optimal rule for the choice of the block length.

AB - We study subsampling estimators for the limit variance σ2=V ar(X1)+2∑∞k=2Cov(X1,Xk) of partial sums of a stationary stochastic process (Xk)k≥1. We establish L2-consistency of a non-overlapping block resampling method. Our results apply to processes that can be represented as functionals of strongly mixing processes. Motivated by recent applications to rank tests, we also study estimators for the series V ar(F(X1))+2∑∞k=2Cov(F(X1),F(Xk)), where F is the distribution function of X1. Simulations illustrate the usefulness of the proposed estimators and of a mean squared error optimal rule for the choice of the block length.

KW - Variance extimation

KW - Weakly dependent Processes

KW - Subsampling techniques

KW - Central limit theorem

KW - Functionals of mixing processes

U2 - 10.1016/j.spl.2012.08.012

DO - 10.1016/j.spl.2012.08.012

M3 - Article

VL - 83

SP - 141

EP - 147

JO - Statistics and Probability Letters

JF - Statistics and Probability Letters

SN - 0167-7152

IS - 1

ER -