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重复显著性检验与序贯检验后估计中的 Anscombe 定理渐近展开AI 解读

Let $x_1, x_2, \cdots$ be independent and normally distributed with unknown mean $\theta$ and variance 1. Let $\tau = \inf \{n \geq 1: |s_n| \geq \sqrt{2a(n + c)}\}$. Then a repeated significance test for a normal mean rejects the hypothesis $\theta = 0$ if and only if $\tau \leq N_0$ for some positive integer $N_0$. The problem we consider is estimation of $\theta$ based on the data $x_1,\cdots, x_T, T = \min\{\tau, N_0\}$. We shall solve this problem by obtaining the…

若干重复显著性检验错误概率的渐近展开AI 解读

Asymptotic expansions for the error probabilities of repeated significance tests about a normal mean are developed. Use of the expansions appears to result in substantially improved numerical accuracy, when compared to the use of the leading term, at least in some important special cases. The expansions are sufficiently refined to show the effect of some simple modifications of the basic procedure, such as requiring an initial sample size.