A smooth block bootstrap for quantile regression with time series
A smooth block bootstrap for quantile regression with time series
复制标题
用于时间序列分位数回归的平滑块引导程序
作者：
Karl B. Gregory;S. Lahiri;D. Nordman
分位数回归允许对超出条件均值的响应分布进行广泛的(有条件的)表征，并且在经济和fi金融应用中越来越受到关注。由于分位数回归估计具有复杂的极限分布，已有几种独立数据设置的Bootstrap方法被提出，其中许多方法涉及平滑步骤以改进Bootstrap近似。目前，对于具有相依数据的分位数回归，在平滑引导方面没有类似的进展。为此，我们建立了一个光滑的锥形块Bootstrap过程来逼近时间序列的分位数回归估计量的分布。这个自举过程涉及重采样中的两轮平滑：通过核平滑技术对单个观测值进行重采样，并通过锥化对重采样的数据块进行平滑。与以前的非平滑版本的块引导以及基于Powell核方差估计器的正态近似相比，平滑引导导致性能改进，后者在应用中很常见。我们的理论结果纠正了分位数回归的(非光滑)移动块Bootstrap的早期和更简单形式证明中的错误，并拓宽了块Bootstrap在弱条件下的有效性。通过数值研究和算例说明了该方法的光滑性。。05和0。05，尺寸n=50、100和200。这表明除了分位数参数估计外，SETBB方法在基于QR的预测问题中具有潜在的实用性。
Quantile regression allows for broad (conditional) characterizations of a response distribution beyond conditional means and is of increasing interest in economic and financial applications. Because quantile regression estimators have complex limiting distributions, several bootstrap methods for the independent data setting have been proposed, many of which involve smoothing steps to improve bootstrap approximations. Currently, no similar advances in smoothed bootstraps exist for quantile regression with dependent data. To this end, we establish a smooth tapered block bootstrap procedure for approximating the distribution of quantile regression estimators for time series. This bootstrap involves two rounds of smoothing in resampling: individual observations are resampled via kernel smoothing techniques and resampled data blocks are smoothed by tapering. The smooth bootstrap results in performance improvements over previous unsmoothed versions of the block bootstrap as well as normal approximations based on Powell’s kernel variance estimator, which are common in application. Our theoretical results correct errors in proofs for earlier and simpler versions of the (unsmoothed) moving blocks bootstrap for quantile regression and broaden the validity of block bootstraps for this problem under weak conditions. We illustrate the smooth bootstrap through numerical studies and examples. . 05 and 0 . 05 for the sizes n = 50, 100 and 200. This demonstrates the potential usefulness of the SETBB method in QR-based forecasting problems in addition to quantile parameter estimation.