Under stationary -mixing dependent samples, we in this article develop a novel nonlinear regression based on mode value for time series sequences to achieve robustness without sacrificing estimation efficiency. The estimation process is built on a kernel-based objective function with a constant bandwidth (tuning parameter) that is independent of sample size and can be adjusted to maximize efficiency. The asymptotic distribution of the resultant estimator is established under suitable conditions, and the convergence rate is demonstrated to be the same as that in nonlinear mean regression. To numerically estimate the kernel mode-based regression, we develop a modified modal-expectation-maximization algorithm in conjunction with Taylor expansion. A robust Wald-type test statistic derived from the resulting estimator is also provided, along with its asymptotic distribution for the null and alternative hypotheses. The local robustness of the proposed estimation procedure is studied using influence function analysis, and the good finite sample performance of the newly suggested model is verified through Monte Carlo simulations. We finally combine the recommended kernel mode-based regression with neural networks to develop a kernel mode-based neural networks model, the performance of which is evidenced by an empirical examination of exchange rate prediction.

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基于非线性核模式的相关数据回归

静止状态下-混合相关样本，我们在本文中开发了一种基于时间序列序列众数的新型非线性回归，以在不牺牲估计效率的情况下实现鲁棒性。估计过程建立在基于内核的目标函数上，该目标函数具有恒定带宽（调整参数），该带宽与样本大小无关，并且可以进行调整以最大限度地提高效率。在适当的条件下建立了所得估计量的渐近分布，并且证明了收敛速度与非线性均值回归中的收敛速度相同。为了对基于核模式的回归进行数值估计，我们结合泰勒展开开发了一种改进的模态期望最大化算法。还提供了从所得估计量导出的稳健 Wald 型检验统计量，以及原假设和备择假设的渐近分布。使用影响函数分析研究了所提出的估计过程的局部鲁棒性，并通过蒙特卡洛模拟验证了新提出的模型的良好有限样本性能。最后，我们将推荐的基于核模式的回归与神经网络相结合，开发了基于核模式的神经网络模型，其性能通过汇率预测的实证检验得到了证明。