In quantifying the complexity characteristics of neurophysiological signals, the most advanced entropy methods still have some inevitable limitations of poor accuracy, robustness, and reliability. To solve these limits, this study proposes a novel entropy estimator, termed cumulative residual symbolic dispersion entropy (CRSDE). Meanwhile, a corresponding multiscale variant, time-shift cumulative residual symbolic dispersion entropy (TCRSDE), is introduced to quantify the time series's irregularity on multiple time scales. The CRSDE starts with an improved symbolic dynamics filter (ISDF) based on the equal probability dividing criterion, mapping a raw time series to symbolic series. Next, embedding theory is applied to derive the dispersion patterns. Finally, the cumulative residual probabilities of all dispersion patterns are counted, and corresponding CRSDE results are calculated. A series of performance validations are executed using synthetic and real-world datasets. The simulation results confirm CRSDE's optimal estimation accuracy and robustness to noise and data length. The findings of EEG dataset demonstrate that CRSDE could realize the best reliability with the lowest root mean square deviation (RMSD; <0.05). In the multiscale version, TCRSDE, a time-shift coarse-graining is introduced. The verification findings confirm that the TCRSDE can avoid incorrect estimates and achieve the best-estimated stability on all scales with the smallest coefficient of variation (CV; <0.01) and shortest running time. Finally, CRSDE method is applied to neonatal sleep EEG. Compared to other methods, CRSDE shows the most significant differences, with all p-values less than 0.01 via a nonparametric Mann-Whitney U test. Meanwhile, CRSDE obtains the highest Hedges' g effect size values and least outliers at three sleep stages. Therefore, CRSDE performs best in quantifying neurodynamics of neonatal sleep stages.

在量化神经生理信号的复杂性特征时，最先进的熵方法仍然存在一些不可避免的局限性，即准确性、鲁棒性和可靠性差。为了解决这些限制，本研究提出了一种新的熵估计器，称为累积残余符号色散熵(CRSDE)。同时，相应的多尺度变体，时移累积残余符号色散熵（TCRSDE），用于量化时间序列在多个时间尺度上的不规则性。CRSDE 从基于等概率划分标准的改进符号动态过滤器 (ISDF) 开始，将原始时间序列映射到符号序列。接下来，应用嵌入理论来推导色散模式。最后统计所有色散模式的累积残差概率，计算出相应的CRSDE结果。使用合成和真实世界的数据集执行一系列性能验证。仿真结果证实了 CRSDE 的最佳估计精度以及对噪声和数据长度的鲁棒性。EEG 数据集的研究结果表明，CRSDE 能够以最低的均方根偏差（RMSD；<0.05）实现最佳可靠性。在多尺度版本 TCRSDE 中，引入了时移粗粒度。验证结果证实，TCRSDE 可以避免错误估计，并以最小的变异系数 (CV; <0.01) 和最短的运行时间在所有尺度上实现最佳估计稳定性。最后将CRSDE方法应用于新生儿睡眠脑电图。与其他方法相比，CRSDE 显示出最显着的差异，所有通过非参数 Mann-Whitney U检验，p值小于 0.01 。同时，CRSDE 在三个睡眠阶段获得了最高的 Hedges 的 g 效应大小值和最小的异常值。因此，CRSDE 在量化新生儿睡眠阶段的神经动力学方面表现最佳。