For time series nonparametric regression models with discontinuities, we propose to use polynomial splines to estimate locations and sizes of jumps in the mean function. Under reasonable conditions, test statistics for the existence of jumps are given and their limiting distributions are derived...

Under weak conditions of smoothness and mixing, we propose spline-backfitted spline (SBS) estimators of the component functions for a nonlinear additive autoregression model that is both computationally expedient for analyzing high dimensional large time series data, and theoretically reliable...

For an exchangeable sequence of random variables taking values in a Polish space, we obtain a necessary and sufficient condition for the large deviation principles with respect to the [tau]-topology of the occupation measure and of the process-level empirical measures.