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.
Publié le : 1992-12-14
Classification:
Time series,
spectral density,
weak dependence,
nonparametric estimation,
resampling methods,
bootstrap,
jackknife,
62M10,
62G05
@article{1176348899,
author = {Politis, Dimitris N. and Romano, Joseph P.},
title = {A General Resampling Scheme for Triangular Arrays of $\alpha$-Mixing Random Variables with Application to the Problem of Spectral Density Estimation},
journal = {Ann. Statist.},
volume = {20},
number = {1},
year = {1992},
pages = { 1985-2007},
language = {en},
url = {http://dml.mathdoc.fr/item/1176348899}
}
Politis, Dimitris N.; Romano, Joseph P. A General Resampling Scheme for Triangular Arrays of $\alpha$-Mixing Random Variables with Application to the Problem of Spectral Density Estimation. Ann. Statist., Tome 20 (1992) no. 1, pp. 1985-2007. http://gdmltest.u-ga.fr/item/1176348899/