Complete consistency for the estimator of nonparametric regression models based on extended negatively dependent errors

On the convergence rates of kernel estimator and hazard estimator for widely dependent samples

“…So, Lemma 2.4 is a generalization of Theorem 4 in Shen ([17], 2013), and it extends the Bernstein-type inequality in Wang ([18], 2015, Lemma 2.2) from END to WOD sequence.…”

Exponential probability inequalities for WNOD random variables and their applications

“…This is the definition of END sequences. For the details about the concept and the probability limit theory of END sequence, one can refer to Liu [9], Chen et al [3], Shen [17], Wang and Chen [34], Wang and Wang [24], Wang et al [28,29,32], Qiu et al [13], and so forth. If both (1.1) and (1.2) hold for g L (n) = g U (n) = 1 for any n ≥ 1, then the random variables {X n , n ≥ 1} are called negatively orthant dependent (NOD, in short).…”

Complete convergence and complete moment convergence for extended negatively dependent random variables

“…Some applications for END sequence have been found. See for example, Liu [8] obtained the precise large deviations for dependent random variables with heavy tails; Liu [9] studied the sufficient and necessary conditions of moderate deviations for dependent random variables with heavy tails; Chen et al [3] established the strong law of large numbers for extend negatively dependent random variables and showed applications to risk theory and renewal theory; Chen et al [4] obtained the precise large deviations of random sums in presence of negative dependence and consistent variation; Shen [11] presented some probability inequalities for END sequences and gave some applications; Wang and Wang [14] studied the precise large deviations for random sums of END real-valued random variables with consistent variation; Wang et al ([18], [19]) obtained some convergence results for weighted sums of END random variables; Wang et al [21] established the complete consistency for the estimator of nonparametric regression models based on END error, and so forth. In this paper, our emphasis will be focused on the complete convergence for weighted sums of arrays of rowwise END random variables.…”