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In this paper, we consider the following nonparametric regression model: $$\begin{aligned} Y_{ni} = f\left( x_{ni}\right) + \varepsilon _{ni},\quad i = 1, 2, \ldots , n,\quad n\ge 1, \end{aligned}$$ Y ni = f x ni + ε ni , i = 1 , 2 , … , n , n ≥ 1 , where $$x_{ni}$$ x ni are known fixed design points from A, where $$A\subset {\mathbb {R}}^d$$ A ⊂ R d...
In this paper, we study the complete f-moment convergence for arrays of rowwise extended negatively dependent (END) random variables. A general result on the complete moment convergence for arrays of rowwise END random variables is established, which generalizes and improves the corresponding ones of Wu et al. (Glasnik Matematički 49(69):447–466, 2014) and Hu et al. (Sankhya A 77(1):1–29, 2015). As...
Some equivalent conditions of complete moment and complete integral convergence for a class of dependent random variables are established. The results obtained in this paper extend the corresponding ones for negatively associated random variables. As applications, we present some results for specific sequences of random variables, such as $$\rho $$ ρ -mixing, $$\rho ^{*}$$ ρ∗ -mixing, $$\varphi $$...
In this paper, we investigate the complete convergence of moving average process $$\sum \nolimits _{i=-\infty }^{\infty }a_iY_{i+n}, n\ge 1$$ ∑ i = - ∞ ∞ a i Y i + n , n ≥ 1 , where $$\{Y_i,-\infty<i<+\infty \}$$ { Y i , - ∞ < i < + ∞ } is a doubly infinite sequence of random variables and $$\{a_n,-\infty<n<+\infty \}$$ { a n , - ∞ < n...
In this paper, the equivalent conditions of complete moment convergence of the maximum partial weighted sums for negatively superadditive dependent (NSD) random variables are established without the assumption of identical distribution. As applications, the complete moment convergence, the complete convergence and strong law of large numbers for NSD random variables are obtained. The results obtained...
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