So far the study of exponential bounds of an empirical process has been restricted to a bounded index class of functions. The case of an unbounded index class of functions is now studied on the basis of a new symmetri...So far the study of exponential bounds of an empirical process has been restricted to a bounded index class of functions. The case of an unbounded index class of functions is now studied on the basis of a new symmetrization idea and a new method of truncating the original probability space; the exponential bounds of the tail probabilities for the supremum of the empirical process over an unbounded class of functions are obtained. The exponential bounds can be used to establish laws of the logarithm for the empirical processes over unbounded classes of functions.展开更多
基金This work was supported partially by the National Natural Science Foundation of China(Grant No.19661001)the Social Science Foundation of Ministry of Education of China.
基金supported partially by the National Natural Science Foundation of China (Grant No. 10471061)the Social Science Foundation of Ministry of Education of China (Grant No. 01JD910001)
文摘So far the study of exponential bounds of an empirical process has been restricted to a bounded index class of functions. The case of an unbounded index class of functions is now studied on the basis of a new symmetrization idea and a new method of truncating the original probability space; the exponential bounds of the tail probabilities for the supremum of the empirical process over an unbounded class of functions are obtained. The exponential bounds can be used to establish laws of the logarithm for the empirical processes over unbounded classes of functions.
