Probability inequalities for sums of NSD random variables and applications

Abstract

In this paper, we obtain the exponential-type inequalities for maximal partial sums of negatively superadditive dependent (NSD) random variables, which extends the corresponding results for independent and negatively associated (NA) random variables. Using these inequalities, we further investigate the weak 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.

Keywords:

• NSD random variable
• generalized linear models
• M-estimates
• weak convergence

Disclosure statement

No potential conflict of interest was reported by the authors.

Author contributions

All authors contributed equally to the writing of this paper. All authors read approved the final manuscript.

Additional information

Funding

Support by National Natural Science Foundation of China (No. 11471105).