The paper considers simultaneous nonparametric inference for a wide class of M-regression models with time-varying coefficients. The covariates and errors of the regression model are tackled as a general class of piece-wise locally stationary time series and are allowed to be cross-dependent. We introduce an integration technique to study the M-estimators, whose limiting properties are disclosed using Bahadur representation and Gaussian approximation theory. Facilitated by a self-convolved bootstrap proposed in this paper, we introduce a unified framework to conduct general classes of Exact Function Tests, Lack-of-fit Tests, and Qualitative Tests for the time-varying coefficient M-regression under complex temporal dynamics. As an application, our method is applied to studying the anthropogenic warming trend and time-varying structures of the ENSO effect using global climate data from 1882 to 2005.

翻译：本文研究了一类具有时变系数的M回归模型的同时非参数推断问题。回归模型的协变量和误差被视为一类分段局部平稳时间序列，并允许存在交叉依赖关系。我们引入了一种积分技术来研究M估计量，并通过Bahadur表示和高斯逼近理论揭示了其极限性质。借助本文提出的自卷积自助法，我们建立了一个统一框架，用于在复杂时间动态下对时变系数M回归进行一般类别的精确函数检验、缺乏拟合检验和定性检验。作为应用，我们将该方法应用于1882年至2005年全球气候数据，研究人为变暖趋势和ENSO效应的时变结构。