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December, 1992 A General Resampling Scheme for Triangular Arrays of $\alpha$-Mixing Random Variables with Application to the Problem of Spectral Density Estimation
Dimitris N. Politis, Joseph P. Romano
Ann. Statist. 20(4): 1985-2007 (December, 1992). DOI: 10.1214/aos/1176348899

Abstract

In 1989 Kunsch introduced a modified bootstrap and jackknife for a statistic which is used to estimate a parameter of the $m$-dimensional joint distribution of stationary and $\alpha$-mixing observations. The modification amounts to resampling whole blocks of consecutive observations, or deleting whole blocks one at a time. Liu and Singh independently proposed (in 1988) the same technique for observations that are $m$-dependent. However, many time-series statistics, notably estimators of the spectral density function, involve parameters of the whole (infinite-dimensional) joint distribution and, hence, do not fit in this framework. In this report we generalize the "moving blocks" resampling scheme of Kunsch and Liu and Singh; a still modified version of the nonparametric bootstrap and jackknife is seen to be valid for general linear statistics that are asymptotically normal and consistent for a parameter of the whole joint distribution. We then apply this result to the problem of estimation of the spectral density.

Citation

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Dimitris N. Politis. Joseph P. Romano. "A General Resampling Scheme for Triangular Arrays of $\alpha$-Mixing Random Variables with Application to the Problem of Spectral Density Estimation." Ann. Statist. 20 (4) 1985 - 2007, December, 1992. https://doi.org/10.1214/aos/1176348899

Information

Published: December, 1992
First available in Project Euclid: 12 April 2007

zbMATH: 0776.62070
MathSciNet: MR1193322
Digital Object Identifier: 10.1214/aos/1176348899

Subjects:
Primary: 62M10
Secondary: 62G05

Rights: Copyright © 1992 Institute of Mathematical Statistics

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Vol.20 • No. 4 • December, 1992
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