### Abstract

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.

Original language | English |
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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 |

### Keywords

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

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## Cite this

Vogel, D., Dehling, H., Fried, R., Sharipov, O., & Wornowizki, M. (2013). Estimation of the Variance of Partial Sums of Dependent Processes.

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