ABSTRACT In sequential analysis, an experimenter may gather information regarding an unknown parameter by observing random samples in successive steps. We emphasize a number of specific parametric models under a variety of loss functions. The total number of observations collected at termination is a positive integer-valued random variable, customarily denoted by . The exact probability distribution of N is often hard to obtain. However, under a set of regulatory conditions, our standardized version of the stopping variable from Definition 2.1 in Section 2.2 would follow a normal distribution in the asymptotic sense. In this article, we first show how these regulatory conditions build upon one another in order to conclude the asymptotic normality of such standardized stopping variable, . We provide exploratory data analysis (EDA) via a number of interesting illustrations obtained through large-scale simulation studies. We demonstrate the broad applicability of purely sequential methodologies included in this article along with the appropriateness of our conclusions regarding the asymptotic normality of the standardized stopping variable as a practical guideline.

中文翻译：

---

EDA 关于标准化顺序停止时间的渐近正态性，第一部分：参数模型

摘要 在顺序分析中，实验者可以通过观察连续步骤中的随机样本来收集有关未知参数的信息。我们强调了各种损失函数下的许多特定参数模型。在终止时收集的观察总数是一个正整数值随机变量，通常用 表示。N 的准确概率分布通常很难获得。然而，在一组监管条件下，我们在第 2.2 节中定义 2.1 中的停止变量的标准化版本将遵循渐近意义上的正态分布。在本文中，我们首先展示这些监管条件如何相互建立，以得出此类标准化停止变量的渐近正态性。我们通过大量通过大规模模拟研究获得的有趣插图提供探索性数据分析 (EDA)。我们证明了本文中包含的纯顺序方法的广泛适用性，以及我们关于标准化停止变量的渐近正态性作为实用指南的结论的适当性。