A General Resampling Scheme for Triangular Arrays of $\alpha$-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 $\alpha$ -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.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.

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分类依据与纠错

A General Resampling Scheme for Triangular Arrays of α\alphaα-Mixing Random Variables with Application to the Problem of Spectral Density EstimationA General Resampling Scheme for Triangular Arrays of $\alpha$-Mixing Random Variables with Application to the Problem of Spectral Density Estimation

代码、数据与补充材料

α 混合随机变量三角阵列的一般重抽样方案及谱密度估计应用

原文摘要

同方向的基础文献

相关领域论文

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A General Resampling Scheme for Triangular Arrays of $\alpha$ -Mixing Random Variables with Application to the Problem of Spectral Density EstimationA General Resampling Scheme for Triangular Arrays of $\alpha$-Mixing Random Variables with Application to the Problem of Spectral Density Estimation