A General Resampling Scheme for Triangular Arrays of α-Mixing Random Variables with Application to the Problem of Spectral Density Estimation
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 α-mixing observations. The modification amounts to resampling whole blocks of consecutive observations, or deleting whole block...
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| Veröffentlicht in: | The Annals of statistics 1992-12, Vol.20 (4), p.1985-2007 |
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| container_end_page | 2007 |
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| container_issue | 4 |
| container_start_page | 1985 |
| container_title | The Annals of statistics |
| container_volume | 20 |
| creator | Politis, Dimitris N. Romano, Joseph P. |
| description | 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 α-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. |
| doi_str_mv | 10.1214/aos/1176348899 |
| format | Article |
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| ispartof | The Annals of statistics, 1992-12, Vol.20 (4), p.1985-2007 |
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| language | eng |
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| source | Jstor Complete Legacy; Elektronische Zeitschriftenbibliothek - Frei zugängliche E-Journals; Project Euclid Complete; JSTOR Mathematics & Statistics |
| subjects | 62G05 62M10 bootstrap Confidence interval Consistent estimators Density estimation Estimators Exact sciences and technology Inference from stochastic processes time series analysis Integers jackknife Mathematics nonparametric estimation Probability and statistics Random variables resampling methods Sample mean Sciences and techniques of general use spectral density Spectral energy distribution Statistical variance Statistics Time series weak dependence |
| title | A General Resampling Scheme for Triangular Arrays of α-Mixing Random Variables with Application to the Problem of Spectral Density Estimation |
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