V2EX empirical process

Empirical Process

定义 Definition

经验过程(empirical process)是概率论与统计学中的一个概念:把样本的经验分布/经验平均与其理论期望之间的随机波动,视为一个随函数或集合变化的随机过程。它常用于研究大样本性质(如一致收敛、中心极限定理的函数形式等)。在更一般语境下也可泛指“以观察数据为基础的过程”,但统计学含义最常见。

发音 Pronunciation (IPA)

/mprkl prss/ (英)
/mprkl prss/ (美)

例句 Examples

We study the empirical process to understand how the sample distribution behaves.
我们研究经验过程,以理解样本分布如何表现。

In modern statistics, empirical process theory provides tools to prove uniform convergence results for many estimators.
在现代统计学中,经验过程理论提供了工具,用来证明许多估计量的“一致收敛”等结果。

词源 Etymology

empirical 来自希腊语 empeirikos,意为“基于经验/观察的”;process 来自拉丁语 processus,意为“向前推进的过程”。合在一起,在统计语境中指“由观测本所诱导、用来刻画随机波动的过程”。

相关词 Related Words

文学与著作 Literary & Notable Works

  • Weak Convergence and Empirical Processes: With Applications to Statistics(Aad van der Vaart & Jon Wellner)
  • Asymptotic Statistics(Aad van der Vaart)
  • Convergence of Probability Measures(Patrick Billingsley,相关章节常与经验过程/弱收敛工具并用)
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