Before revision:  We try to investigate the large sample properties of general L-statistics based on i.i.d cases and apply them to our kernel based estimatorof SRM . We prove that the estimator is strongly consistent and the estimator is asymptotically normal.
After revision:  We try to investigate the large sample properties of general L-statistics based on i.i.d and dependent observations and apply them to our kernel based estimatorof SRM . We prove that the estimator is strongly consistent and the estimator is asymptotically normal.