Distribution-Free Confidence Intervals for Conditional Probabilities and Ratios of Expectations
针对两个未知均值的比值（如条件概率）提出置信区间，适用于独立同分布且有界有序的随机对，尤其当分量可表示为伯努利与有界随机变量乘积时。区间基于无分布误差界，适用于任意样本量，渐近宽度与中心极限定理区间相同。实验表明，小样本（≤50）下区间保守且覆盖更优。
Many simulation experiments are concerned with the estimation of a ratio of two unknown means, the estimation of a conditional probability being an example. We propose confidence intervals for the case in which the ratio is estimated by using independent, identically distributed random pairs with bounded and ordered components. Emphasis is given to the case in which each component can be expressed as the product of a Bernoulli and a bounded random variable. The proposed intervals result from distribution-free bounds on error probabilities, are valid for every sample size, and their asymptotic width decreases at the same rate as that of confidence intervals based on the central limit theorem. We evaluate their performance by means of two experiments. The first considers the estimation of the probability that a path in a directed a network is shortest while the second considers the estimation of the distribution of the inventory level in a stationary inventory system with periodic review. The experiments show that the intervals are conservative with superior coverage for small sample sizes (≤50).