On complete convergence for widely orthant-dependent random variables and its applications in nonparametric regression models

Complete Moment Convergence for Arrays of Rowwise Negatively Associated Random Variables and Its Application in Non-Parametric Regression Model

“…We choose casually that θ = 0.6, k n = n 2/3 , l = 3/2 and q = 8 in Theorem 4.1. As is stated in Wang et al [29], conditions (A 1 )-(A 3 ) hold true and it is easy to check that (4.3) is satisfied. Taking the points x = 0.25, 0.5, 0.75 and the sample sizes n as n = 50, 100, 200, 500, respectively, we use R software to compute g n (x) − g(x) with g(x) = x 2 and g(x) = sin x for 1000 times and obtain the Boxplots of g n (x) − g(x) in Figures 1-6 and the Mean Square Error (MSE) of g n (x) in Table 1.…”

“…The above estimator with constant weight was first proposed by Stone [24], adapted by Georgiev [6] and then constantly studied by many authors. One can refer to Roussas [18], Fan [5], Roussas, Tran, and Ioannides [19], Tran et al [26], Hu et al [9], Liang and Jing [16], Wang et al [29], Wang and Si [28], Shen, Zhang, and Volodin [21], Liang and Baek [15], Yang et al [31], among others.…”

On the Strong Law of Large Numbers for Weighted Sums of Negatively Superadditive Dependent Random Variables

“…The proof is standard, so we omit the details. One can refer to Wu [21] or Wang et al [19] for instance.…”

Exponential probability inequalities for WNOD random variables and their applications

“…There are only some literatures studying the probability limiting behavior of WNOD random variables, such as Wang et al [23], Wang and Cheng [34], Wang et al [35], Liu et al [10], Chen et al [4], Shen [19], Qiu and Chen [12], Qiu and Hu [14], Wang et al [31], Yang et al [43], and so on. In these literatures, Wang et al [31] made great contribution to the probability limit theory and statistical large sample theory for WNOD random variables; they established some general results on complete convergence for weighted sums of arrays of rowwise WNOD random variables and presented some sufficient conditions to prove the complete consistency for the estimator of nonparametric regression model based on WNOD errors.…”