A nonparametric method is proposed for estimating the quantile spectra and cross-spectra introduced in Li (2012; 2014) as bivariate functions of frequency and quantile level. The method is based on the quantile discrete Fourier transform (QDFT) defined by trigonometric quantile regression and the quantile series (QSER) defined by the inverse Fourier transform of the QDFT. A nonparametric spectral estimator is constructed from the autocovariance function of the QSER using the lag-window (LW) approach. Smoothing techniques are also employed to reduce the statistical variability of the LW estimator across quantiles when the underlying spectrum varies smoothly with respect to the quantile level. The performance of the proposed estimation method is evaluated through a simulation study.

翻译：本文提出了一种非参数方法，用于估计 Li (2012; 2014) 中引入的作为频率与分位数水平二元函数的分位数谱与交叉谱。该方法基于由三角分位数回归定义的分位数离散傅里叶变换，以及由 QDFT 的傅里叶逆变换定义的分位数序列。利用滞后窗方法，从 QSER 的自协方差函数构造了一个非参数谱估计量。当基础谱随分位数水平平滑变化时，还采用了平滑技术来降低 LW 估计量在不同分位数间的统计变异性。通过模拟研究评估了所提估计方法的性能。