Sharp large deviations for sums of bounded from above random variables
Tóm tắt
We show large deviation expansions for sums of independent and bounded from above random variables. Our moderate deviation expansions are similar to those of Cramér (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.
Tài liệu tham khảo
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