摘要
We show large deviation expansions for sums of independent and bounded from above random variables. Our moderate deviation expansions are similar to those of Cram′er(1938), Bahadur and Ranga Rao(1960), and Sakhanenko(1991). In particular, our results extend Talagrand's inequality from bounded random variables to random variables having finite(2 + δ)-th moments, where δ∈(0, 1]. As a consequence,we obtain an improvement of Hoeffding's inequality. Applications to linear regression, self-normalized large deviations and t-statistic are also discussed.
We show large deviation expansions for sums of independent and bounded from above random variables. Our moderate deviation expansions are similar to those of Cram′er（1938）, Bahadur and Ranga Rao（1960）, and Sakhanenko（1991）. In particular, our results extend Talagrand＇s inequality from bounded random variables to random variables having finite（2 ＋ δ）-th moments, where δ∈（0, 1]. As a consequence,we obtain an improvement of Hoeffding＇s inequality. Applications to linear regression, self-normalized large deviations and t-statistic are also discussed.
基金
supported by National Natural Science Foundation of China (Grant Nos. 11601375 and 11626250)
