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This article mainly studies the strong convergence properties for randomly weighted maximum partial sums of arrays of row-wise extended negatively dependent (END, for short) random variables, including the complete moment convergence and complete f-moment convergence. The results obtained in this paper extend the corresponding ones in the literature. As an application, we investigate the complete consistency of the estimators of nonparametric regression models based on END random errors by using the complete convergence that we established. Then we provide comprehensive simulation studies to demonstrate the validity of the theoretical results based on the finite sample performance. Finally, an application to a real data set is illustrated. [ABSTRACT FROM AUTHOR]

In this paper, we study the complete moment convergence for arrays of rowwise m-extended negatively dependent (m-END) random variables, which generalizes some corresponding ones for complete convergence. We also give an application to non-parametric regression model based on m-END errors by using the complete convergence that we establish. Finally, the choice of the fixed design points and the weight functions for the nearest neighbor estimator are proposed. We also provide a numerical simulation to verify the validity of our theoretical result. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the parametric component and nonparametric component estimators in a semiparametric regression model based on φ -mixing random errors. The r-th mean consistency and uniform consistency are established under some suitable conditions. Finally, a simulation to study the numerical performance of the consistency for the nearest neighbor weight function estimators is provided. The results obtained in the paper complement the existing ones of independent random errors to the case of φ -mixing random errors. [ABSTRACT FROM AUTHOR]