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A nonparametric resampling procedure for multivariate confidence regions in time series analysis. (English) Zbl 0744.62066
Computing science and statistics, Proc. 22nd Symp. Interface, East Lansing/MI (USA) 1990, 98-103 (1992).
Summary: [For the entire collection see Zbl 0741.00075.]
The nonparametric bootstrap and jackknife 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 H. R. Künsch [Ann. Stat. 17, No. 3, 1217-1241 (1989; Zbl 0684.62035)] and independently by R. Y. Liu and K. Singh in an unpublished manuscript, in order to obtain consistent bootstrap and jacknife procedures for a parameter of the $$m$$- dimensional joint distribution of the observations.
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 $$\alpha$$-mixing observations. A notable example of such parameters is given by the spectral density function evaluated on a grid of points.

##### MSC:
 62G09 Nonparametric statistical resampling methods 62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH) 62G15 Nonparametric tolerance and confidence regions