AI 中文总结
本文针对含单个索引随机异常值的2ⁿᴿ个序列，在ℋ₀误差概率不趋近于1的约束下，推导了ℋ₀与ℋ₁间检验的Chernoff-Stein型指数，即ℋ₁下决策误差概率的最快指数衰减率。
AI 中文摘要
在长度为n的2ⁿᴿ个随机序列中，存在一个索引随机的异常值序列。在假设ℋ₀下，该异常值的分量服从独立同分布（IID）的Q₀分布；在假设ℋ₁下，其分量服从独立同分布（IID）的Q₁分布。其余(2ⁿᴿ−1)个序列相互独立，且与异常值无关，在两个假设下均服从独立同分布（IID）的P分布。基于对所有2ⁿᴿ个序列的观测，需在ℋ₀和ℋ₁之间作出决策。在ℋ₀下的决策误差概率需被限制为不趋近于1的约束下，本文确定了ℋ₁下决策误差概率的最快指数衰减率。
英文摘要
Among $2^{nR}$ length-$n$ random sequences, one sequence is an outlier whose index is random. Under hypothesis $\mathcal{H}_0$, the components of the outlier are independent and identically distributed (IID) according to $Q_0$, whereas under hypothesis $\mathcal{H}_1$ they are IID according to $Q_1$. The remaining $(2^{nR}-1)$ sequences are mutually independent, independent of the outlier, and IID according to $P$ under both hypotheses. Based on the observation of all $2^{nR}$ sequences, one wishes to decide between $\mathcal{H}_0$ and $\mathcal{H}_1$. Under the constraint that the decision error probability under $\mathcal{H}_0$ must be bounded away from $1$, we determine the fastest exponential decay rate of the decision error probability under $\mathcal{H}_1$.
