Abstract: We establish Nagaev and Rosenthal-type inequalities for dependent random variables. The imposed dependence conditions, which are expressed in terms of functional dependence measures, are directly related to the physical mechanisms of the underlying processes and are easy to work with. Our results are applied to nonlinear time series and kernel density estimates of linear processes.
Key words and phrases: m-dependence approximation, Nagaev inequality, nonlinear process, non-stationary process, physical dependence measure, Rosenthal inequality.