Approximate Tolerance Intervals, Based on Maximum Likelihood Estimates
本文提出一种修正方法，在估计参数后构造容忍区间时加入1/n阶校正项，使区间长度增加以反映参数估计的不确定性，并通过两个例子说明该方法。
Abstract Let X 1, …, Xn be independent random variables with distributions depending on a possibly multidimensional θ. Let Y be an unobserved continuously distributed random variable whose distribution depends on θ. A tolerance interval for Y is desired, satisfying P[Y ε I(X 1, …, Xn )] = β. A naive interval would estimate θ from the X's and construct the interval assuming that the estimate is exactly correct. This article assumes standard regularity conditions and uses Taylor approximations to construct correction terms of order 1/n. The resulting interval is longer than the naive interval because it takes into account the uncertainty in the estimate of θ. Two examples, one simple and one complex, illustrate the method.