论文标题
在CLT中收敛速率的不均匀估计中，常数的下限
Lower bounds for the constants in non-uniform estimates of the rate of convergence in the CLT
论文作者
论文摘要
我们对Nagaev-Bikelis和Bikelis-Petrov不平等的常数进行比较分析，这些不平等现象对中央限制定理的收敛速率的不均匀估计值，用于具有$ 2+δ$的独立随机变量的总和，具有$ 2+Δ$ in $Δ\ in [0,1,1] $。我们为上述常数以及Nagaev-Bikelis不平等的结构改进的常数提供了下限。 Nagaev-Bikelis的不平等及其结构改进的下限是依赖$δ$和结构参数$ s $以及相对于$δ$和$ s $的均匀的。首次提出了$Δ<1 $的Nagaev-Bikelis'常数和Bikelis-Petrov的不平等现象的下限。
We conduct a comparative analysis of the constants in the Nagaev-Bikelis and Bikelis-Petrov inequalities which establish non-uniform estimates of the rate of convergence in the central limit theorem for sums of independent random variables possessing finite absolute moments of order $2+δ$ with $δ\in[0,1]$. We provide lower bounds for the above constants and also for the constants in the structural improvements of Nagaev-Bikelis' inequality. The lower bounds in Nagaev-Bikelis' inequality and it's structural improvements are given in dependence on $δ$ and a structural parameter $s$ as well as uniform with respect to both $δ$ and $s$. Lower bounds for the constants in Nagaev-Bikelis' with $δ<1$ and Bikelis-Petrov's inequalities are presented for the first time.
