Some Large Deviation Inequalities For NA Sequences And Martingales

Large deviation inequalities have a lot of applications on statistical influence,re-liability theory,time series analysis and so on.In this thesis,we give some large devi-ation inequalities for NA sequences and self-normalized martingales.In the first chap-ter,we introduce the background,present situation and content of the research in this thesis.In the second chapter,we consider some large deviation inequalities for NA sequences under various moment conditions.When the random variables have finite p-th moments or have week moments of order p?2,we establish the Fuk-Nagaev type inequalities.When the random variables have semi-exponential moments,we give a semi-exponential inequality.When the random variables are bounded,we obtain the Rio type inequality.When E[ea[Xi]p]<?(p>1),we establish an exponential inequality.At the end of this chapter,we introduce an application of the Rio type inequality.In the third chapter,we consider the Dzhaparidze-van Zanten type inequalities for self-normalized martingales with difference squared integrable or differences non-squared integrable.At the end of this chapter,we present some applications of large deviation inequalities to t-statistic and linear regressions.