Complete f-moment convergence for arrays of random variables and its applications in semiparametric and EV regression models

We study the complete f-moment convergence for arrays of rowwise random variables satisfying a Rosenthal type moment inequality, and then establish general results on the complete moment convergence and complete convergence for partial sums and weighted sums of arrays of rowwise random variables. As applications, we further describe the statistical properties of complete f-moment convergence in both semiparametric regression models and simple linear errors-in-variables models. The asymptotic properties for estimators are established. We also provide some simulations to verify the validity of the theoretical results.