自正则化鞅的Dzhaparidze-van Zanten型不等式

Dzhaparidze-van Zanten type inequalities for self-normalized martingales

将Dzhaparidze-van Zanten型不等式推广到了自正则化鞅的情形,分别考虑鞅差平方可积和非平方可积鞅的Dzhaparidze-vanZanten型不等式,给出了鞅差是左重尾的自正则化鞅的一个偏差不等式.最后讨论了部分不等式在t-统计和线性回归方面的应用.

Some Dzhaparidze-van Zanten type inequalities are derived for self-normalized martingales.The Dzhaparidze-van Zanten inequalities for self-normalized martingales with differences squared integrable or differences not squared integrable are discussed,and a deviation inequality is also given for self-normalized martingales with differences heavy on left.Finally,some applications on t-statistic and linear regressions are discussed.