Probability Inequalities For Sums Of NSD Random Sequence And Applications

In this paper,we obtain the exponential-type inequalities for maximal partial sums of negatively superadditive dependent(NSD)random variables.Using the truncation technique of NSD random variables and the method Fuc-Nagaev type probability inequality,we discuss the limit properties for sums of random variables,some important exponential type probability inequalities and moment inequalities are obtained.These inequalities extends the corresponding results for independent and negatively associated(NA)random variables,and also improve the related conclusions such as Fuc,Hu and Su.Using these inequalities,we further investigate the weak convergence and strong convergence of the M-estimators in the generalized linear model with NSD errors,which generalize and improve the corresponding results of the independent random errors to that of NSD random errors.In chapter 2,using the truncation technique of NSD random variables and the method Fuc-Nagaev type probability inequality,unilateral inequalities and bilateral inequalities are derived,and the proofs of these inequalities are given.In chapter 3,using the results of the second chapter,under certain conditions,we obtain the probability inequalities of the probability inequalities of the random variables in the special cases,and further generalize the probability inequalities of independent random variables and NA random variables.In chapter 4,the results of 2-3 chapters are applied to the generalized linear model with NSD error,and the weak convergence and strong convergence of unknown parameters of the generalized model are obtained.