Uniform convergence of estimator for nonparametric regression with dependent data

In this paper, the authors investigate the internal estimator of nonparametric regression with dependent data such as α-mixing. Under suitable conditions such as the arithmetically α-mixing and E|Y₁|ˢ<∞ ( $s>2$ ), the convergence rate |mₙ(x)-m(x)|=OP(aₙ)+O(h²) and uniform convergence rate _x∈ Sf^|mₙ(x)-m(x)|=Oₚ(aₙ)+O(h²) are presented, if aₙ=√ln nnhᵈ→0 . We generalize some results in Shen and Xie (Stat. Probab. Lett. 83:1915-1925, 2013).