A maximal moment inequality for -mixing sequences and its applications

Maximal Inequalities and an Application Under a Weak Dependence

“…Again we apply the inequality in (13) to E|Y j | q , E|Z j | q and E max 1≤l≤k (j−1)k+l i=(j−1)k+1X i q in (11). We repeat ℓ times, (ℓ positive integer), in this way to obtain…”

“…For mixing sequences, Utev and Peligrad [12], Yang [15], Xing et al [13] and Xuejun et al [14] among others obtained maximal moment inequalities with various applications.…”

“…Our results are derived using the Roussas-Ioannides-type inequalities for the ψ-weak dependence sequences, which has been recently established by Hwang and Shin [7]. Maximal moment inequalities are applied to obtain diverse probabilistic results such as CLT, FCLT, LLN, and LIL as studied by many authors for strong mixing cases, as well as statistical results such as uniform convergence of nonparametric kernel estimators and asymptotic normality of general linear estimator for the fixed design regression as studied by Yang [15] and Xing et al [13] for strong mixing cases. Our results can be applied to obtain those applications under the ψ-weak dependence.…”

Berry-Esseen bounds for wavelet estimator in semiparametric regression model with linear process errors

“…Recently, Yang and Li [8][9][10] and Xing et al [11][12][13] established moment bounds and maximal moment inequality for partial sums for strong mixing sequences and their application. In this article, we study the Berry-Esseen type bounds for wavelet estimators of b and g(·) in model (1.1) based linear process errors {ε i } satisfying the following basic assumption (A1).…”