UNIFORM CONVERGENCE RATES OVER MAXIMAL DOMAINS IN STRUCTURAL NONPARAMETRIC COINTEGRATING REGRESSION
研究了结构非线性协整回归模型中核回归估计量的一致收敛速度，将现有结果推广到更宽的域、允许误差序列相关且与回归变量交叉相关、以及数据依赖带宽，回归变量可具有分数积分和无限方差。
This paper presents uniform convergence rates for kernel regression estimators, in the setting of a structural nonlinear cointegrating regression model. We generalise the existing literature in three ways. First, the domain to which these rates apply is much wider than the domains that have been considered in the existing literature, and can be chosen so as to contain as large a fraction of the sample as desired in the limit. Second, our results allow the regression disturbance to be serially correlated, and cross-correlated with the regressor; previous work on this problem (of obtaining uniform rates) having been confined entirely to the setting of an exogenous regressor. Third, we permit the bandwidth to be data-dependent, requiring it to satisfy only certain weak asymptotic shrinkage conditions. Our assumptions on the regressor process are consistent with a very broad range of departures from the standard unit root autoregressive model, allowing the regressor to be fractionally integrated, and to have an infinite variance (and even infinite lower-order moments).