When addressing various financial problems,such as estimating stock portfolio risk,it is necessary to derive the distribution of the sum of the dependent random variables.Although deriving this distribution requires i...When addressing various financial problems,such as estimating stock portfolio risk,it is necessary to derive the distribution of the sum of the dependent random variables.Although deriving this distribution requires identifying the joint distribution of these random variables,exact estimation of the joint distribution of dependent random variables is difficult.Therefore,in recent years,studies have been conducted on the bound of the sum of dependent random variables with dependence uncertainty.In this study,we obtain an improved Hoeffding inequality for dependent bounded variables.Further,we expand the above result to the case of sub-Gaussian random variables.展开更多
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...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.展开更多
基金This work was supported by JSPS Grant-in-Aid for Young Scientists(Grant No.18K12873)Waseda University Grants for Special Research Projects(“Tokutei Kadai”)(Grant No.2019C-688).
文摘When addressing various financial problems,such as estimating stock portfolio risk,it is necessary to derive the distribution of the sum of the dependent random variables.Although deriving this distribution requires identifying the joint distribution of these random variables,exact estimation of the joint distribution of dependent random variables is difficult.Therefore,in recent years,studies have been conducted on the bound of the sum of dependent random variables with dependence uncertainty.In this study,we obtain an improved Hoeffding inequality for dependent bounded variables.Further,we expand the above result to the case of sub-Gaussian random variables.
基金supported by National Natural Science Foundation of China (Grant Nos. 11601375 and 11626250)
文摘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.
