A UNIFORM LAW OF LARGE NUMBERS FOR DEPENDENT AND HETEROGENEOUS DATA PROCESSES
A UNIFORM LAW OF LARGE NUMBERS FOR DEPENDENT AND HETEROGENEOUS DATA PROCESSES
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DOI：
10.2307/1911058
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发表时间：
1989-05
期刊：
影响因子：
6.1
通讯作者：
B. M. Pötscher;I. Prucha
中科院分区：
文献类型：
--
作者：
B. M. Pötscher;I. Prucha
大数定律（ULLNs）考虑如下形式的和：$n^{-1}\sum_{t = 1}^{n}[q_t(z_t,\theta) - Eq_t(z_t,\theta)]$，其中$(z_t)$表示一个在空间$Z$中取值的随机数据生成过程，$\theta$是参数空间$\Theta$中的一个元素，并且$q_t: Z\times\Theta\rightarrow R$。大数定律提供了在何种条件下上述和在参数空间上一致收敛到零的条件。本文的目的是引入一个新的通用大数定律。它保持了一组相对容易验证的假设，同时允许对经济学中各种感兴趣的估计量和模型进行分析。
Uniform laws of large numbers (ULLNs) consider sums of the form: n −1 Σ t n =1 [q t (z t , θ)-Eq t (z t , θ)], where (z t ) denotes a stochastic data generating process that takes its values in a space Z, θ is an element of the parameter space Θ, and q t : Z×Θ→R. ULLNs provide conditions under which the above sum converges to zero uniformly over the parameter space. The purpose of the present note is to introduce a new generic ULLN. It maintains a set of assumptions that is relatively easy to verify and allows at the same time the analysis of a wide variety of estimators and models of interest in economics