GENERIC UNIFORM-CONVERGENCE
GENERIC UNIFORM-CONVERGENCE
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DOI：
10.1017/s0266466600012780
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发表时间：
1992-06-01
影响因子：
0.8
通讯作者：
ANDREWS, DWK
中科院分区：
文献类型：
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作者：
ANDREWS, DWK
本文给出了几个包含广义一致大数定律的广义一致收敛结果。 这些结果提供了几乎必然或依概率将点态收敛加强为一致收敛的条件。 这些结果对于建立估计量和检验统计量的渐近性质是有用的，它们具有以下性质：（1）推广了Newey [15]的结果，使其不仅包含依概率收敛，而且包含几乎必然收敛;（2）适用于完全有界的参数空间（而不仅仅是紧致参数空间），（3）他们为一般的一致大数定律引入了一组条件，该定律具有给出i.i.d.上下文，但适用于一些依赖的非同分布的上下文中，以及（4）他们纳入和扩展的主要结果在文献中的简约的方式。
This paper presents several generic uniform convergence results that include generic uniform laws of large numbers. These results provide conditions under which pointwise convergence almost surely or in probability can be strengthened to uniform convergence. The results are useful for establishing asymptotic properties of estimators and test statistics.The results given here have the following attributes, (1) they extend results of Newey [15] to cover convergence almost surely as well as convergence in probability, (2) they apply to totally bounded parameter spaces (rather than just to compact parameter spaces), (3) they introduce a set of conditions for a generic uniform law of large numbers that has the attribute of giving the weakest conditions available for i.i.d. contexts, but which apply in some dependent nonidentically distributed contexts as well, and (4) they incorporate and extend the main results in the literature in a parsimonious fashion.