Estimation of the variance of partial sums of dependent processes
AbstractWe study subsampling estimators for the limit variance σ2=V ar(X1)+2∑k=2∞Cov(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=2∞Cov(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.
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Bibliographic InfoArticle provided by Elsevier in its journal Statistics & Probability Letters.
Volume (Year): 83 (2013)
Issue (Month): 1 ()
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- Christophe Croux & Catherine Dehon, 2010.
"Influence functions of the Spearman and Kendall correlation measures,"
Statistical Methods and Applications,
Springer, vol. 19(4), pages 497-515, November.
- Croux, C. & Dehon, C., 2010. "Influence Functions of the Spearman and Kendall Correlation Measures," Discussion Paper 2010-40, Tilburg University, Center for Economic Research.
- Jong, R.M. de & Davidson, J., 1996.
"Consistency of Kernel Estimators of Heteroscedastic and Autocorrelated Covariance Matrices,"
1996-52, Tilburg University, Center for Economic Research.
- Robert M. De Jong & James Davidson, 2000. "Consistency of Kernel Estimators of Heteroscedastic and Autocorrelated Covariance Matrices," Econometrica, Econometric Society, vol. 68(2), pages 407-424, March.
- Peligrad, M. & Shao, Q. M., 1995. "Estimation of the Variance of Partial Sums for [rho]-Mixing Random Variables," Journal of Multivariate Analysis, Elsevier, vol. 52(1), pages 140-157, January.
- Doukhan, Paul & Louhichi, Sana, 1999. "A new weak dependence condition and applications to moment inequalities," Stochastic Processes and their Applications, Elsevier, vol. 84(2), pages 313-342, December.
- Dehling, Herold & Fried, Roland, 2012. "Asymptotic distribution of two-sample empirical U-quantiles with applications to robust tests for shifts in location," Journal of Multivariate Analysis, Elsevier, vol. 105(1), pages 124-140.
- Peligard, Magda & Suresh, Ram, 1995. "Estimation of variance of partial sums of an associated sequence of random variables," Stochastic Processes and their Applications, Elsevier, vol. 56(2), pages 307-319, April.
- Shao, Qi-Man & Yu, Hao, 1993. "Bootstrapping the sample means for stationary mixing sequences," Stochastic Processes and their Applications, Elsevier, vol. 48(1), pages 175-190, October.
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