Almost Sure Central Limit Theorems for Stationary Bootstrap Mean

- Journal title : Communications for Statistical Applications and Methods
- Volume 20, Issue 3, 2013, pp.193-197
- Publisher : The Korean Statistical Society
- DOI : 10.5351/CSAM.2013.20.3.193

Title & Authors

Almost Sure Central Limit Theorems for Stationary Bootstrap Mean

Hwang, Eunju; Shin, Dong Wan;

Hwang, Eunju; Shin, Dong Wan;

Abstract

Almost sure central limit theorems are established for a stationary bootstrap sample mean of strong mixing processes. Both weak and strong consistencies are obtained.

Keywords

Stationary bootstrap;almost sure central limit theorem;

Language

English

References

1.

Berkes, I. (1995). On the almost sure central limit theorem and domains of attraction, Probability Theory and Related Fields, 102, 1-18.

2.

Berkes, I. and Csaki, E. (2001). A universal result in almost sure central limit theory, Stochastic Processes and their Applications, 94, 105-134.

3.

Berkes, I. and Dehling, H. (1993). Some limit theorems in log density, Annals of Probability, 21, 1640-1670.

4.

Berkes, I. and Dehling, H. (1994). On the almost sure central limit theorem for random variables with infinite variance, Journal of Theoretical Probability, 7, 667-680.

5.

Billingsley, P. (1968). Convergence of Probability Measures, Wiley, New York.

6.

Brosamler, G. A. (1988). An almost everywhere central limit theorem, Mathematical Proceedings of the Cambridge Philosophical Society, 104, 561-574.

7.

Chen, S. and Lin, Z. (2008). Almost sure central limit theorems for functionals of absolutely regular processes with application to U-statistics, Journal of Mathematical Analysis and Applications, 340, 1120-1126.

8.

Doukhan, P. and Louhichi, S. (1999). A new weak dependence condition and applications to moment inequalities, Stochastic Processes and their Applications, 84, 313-342.

9.

Dudzinski, M. (2003). A note on the almost sure central limit theorem for some dependent random variables, Statistics & Probability Letters, 61, 31-40.

10.

Hwang, E. and Shin, D. W. (2012). Strong consistency of the stationary bootstrap under ${\psi}$ -weak dependence, Statistics & Probability Letters, 82, 488-495.

11.

Lacey, M. P. and Philipp, W. (1990). A note on the almost sure central limit theorem, Statistics & Probability Letters, 9, 201-205.

12.

Lahiri, S. N. (2003). Resampling Methods for Dependent Data, Springer Series in Statistics, Springer, New York.

13.

Lesigne, E. (1999). Almost sure central limit theorem for strictly stationary processes, Proceedings of the American Mathematical Society, 128, 1751-1759.

14.

Matula, P. (1998). On the almost sure central limit theorem for associated random variables, Probability and Mathematical Statistics, 18, 411-416.

15.

Paparoditis, E. and Politis, D. (2003). Residual-based block bootstrap for unit root testing, Econometrica, 71, 813-855.

16.

Parker, C., Paparoditis, E. and Politis, D. N. (2006). Unit root testing via the stationary bootstrap, Journal of Econometrics, 133, 601-638.

17.

Peligrad, M. and Sho, Q. M. (1995). A note on the almost sure central limit theorem for weakly dependent random variables, Statistics & Probability Letters, 22, 131-136.

18.

Politis, D. N. and Romano, J. P. (1994). The stationary bootstrap, Journal of the American Statistical Association, 89, 1303-1313.