Proceedings of the American Mathematical Society

Author(s): Patrice Bertail; Anthony Gamst; Dimitris N. Politis
Journal: Proc. Amer. Math. Soc. 129 (2001), 551-557.
MSC (1991): Primary 60F05; Secondary 60F10
Posted: July 27, 2000
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In Politis and Romano (1994) the subsampling methodology was put forth for approximating the sampling distribution (and the corresponding quantiles) of general statistics from i.i.d. and stationary data. In this note, we address the question of how well the subsampling distribution approximates the tail of the target distribution. In the regular setting of the sample mean of an

-dependent sequence we show a moderate deviation property of the subsampling distribution.

1.: Andrews, D. and Pollard, D. (1994), An introduction to functional central limit theorems for dependent stochastic processes, Int. Stat. Rev., 62, 119-132.
2.: Heinrich, L. (1982), A method for the derivation of limit theorems for sums of -dependent random variables, Z. Wahrsch. verw. Geb., 60, 501-515. MR 83j:60026
3.: Heinrich, L. (1984), Non-uniform estimates and asymptotic expansions of the remainder in the central limit theorem for -dependent random variables, Math. Nachr. 115, 7-20. MR 85k:60033
4.: Jing, B.Y. (1997), On the relative performance of the block bootstrap for dependent data, Comm. Statist. --Theory and Methods, vol. 26, 1313-1328. MR 98j:62034
5.: Liu, R. and Singh, K. (1992), Moving blocks jackknife and bootstrap capture weak dependence, In Exploring the limits of bootstrap, edited by R. LePage and L. Billard, John Wiley, New York, pp. 225-248. MR 94f:62079
6.: Politis, D.N. and Romano, J.P.(1994). `Large Sample Confidence Regions Based on Subsamples under Minimal Assumptions', Ann. Statist., vol. 22, No. 4, 2031-2050. MR 96b:62078
7.: Pollard, D. (1984), Convergence of Stochastic Processes, Springer Verlag, New York. MR 86i:60074
8.: Pollard, D. (1991), Bracketing methods in statistics and econometrics, in Nonparametric and Semiparametric Methods in Econometrics and Statistics, Cambridge University Press, Cambridge. MR 93m:62056

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 60F05, 60F10

Patrice Bertail
Affiliation: INRA-CORELA, 65, Bd. de Brandebourg, 34205 Ivry-Seine, France

Anthony Gamst
Affiliation: Department of Mathematics, University of California at San Diego, La Jolla, California 92093-0112
Email: acgamst@osiris.ucsd.edu

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