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A Nonparametric Resampling Procedure for Multivariate Confidence Regions in Time Series Analysis

In: Computing Science and Statistics

Author

Listed:
  • Dimitris N. Politis

    (Purdue University, Department of Statistics)

  • Joseph P. Romano

    (Stanford University, Department of Statistics)

Abstract

The nonparametric bootstrap and jackknife (cf. Efron (1979)) have been proven to be powerful tools for approximating the sampling distribution and variance of complicated statistics defined on a sequence of i.i.d. random variables. In the context of weakly dependent stationary observations, a block-resampling scheme was introduced by Künsch(1989) and independently by Liu and Singh(1988), in order to obtain consistent bootstrap and jackknife procedures for a parameter of the m-dimensional joint distribution of the observations. In this paper we discuss a ‘blocks of blocks’ resampling scheme that yields consistent procedures even for multivariate parameters of the whole (infinite-dimensional) joint distribution of stationary and α-mixing observations. A notable example of such parameters is given by the spectral density function evaluated on a grid of points.

Suggested Citation

  • Dimitris N. Politis & Joseph P. Romano, 1992. "A Nonparametric Resampling Procedure for Multivariate Confidence Regions in Time Series Analysis," Springer Books, in: Connie Page & Raoul LePage (ed.), Computing Science and Statistics, pages 98-103, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4612-2856-1_12
    DOI: 10.1007/978-1-4612-2856-1_12
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