MARTINGALE LIMIT THEOREM REVISITED AND NONLINEAR COINTEGRATING REGRESSION
针对一类鞅，在条件方差依分布收敛下建立了混合正态分布的收敛性，放宽了经典鞅极限定理的条件，并应用于非线性协整回归模型中核估计量的极限行为分析。
For a certain class of martingales, convergence to a mixture of normal distributions is established under convergence in distribution for the conditional variance. This is less restrictive in comparison with the classical martingale limit theorem, where one generally requires convergence in probability. The extension partially removes a barrier in the applications of the classical martingale limit theorem to nonparametric estimation and inference with nonstationarity and enhances the effectiveness of the classical martingale limit theorem as one of the main tools to investigate asymptotics in statistics, econometrics, and other fields. The main result is applied to investigate limit behavior of the conventional kernel estimator in a nonlinear cointegrating regression model, which improves existing works in the literature.