Allocation of Effort in Monte Carlo Simulation for Power of Permutation Tests
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置换检验功效蒙特卡洛模拟中的计算投入分配
- 研究问题
- 在固定计算预算下，模拟置换检验功效时应如何分配外层数据生成次数与内层置换次数，以控制估计误差？
- 方法与思路
- 作者以已知的内外层计算成本建立预算约束，推导 p 值分布估计的均方误差，并据此选择内层置换次数。
- 材料陈述的贡献
- 摘要给出一般均方误差表达式，并称在备择接近原假设时，最优次数由四次多项式确定，另分析外层成本可忽略的情形。
- 阅读关注点
- 应核对优化对象与功效估计的关系、接近原假设的近似条件、成本设定，以及最优次数取整后的实际分配。
- 阅读边界
- 仅据版本未注明的 OpenAlex 索引摘要；特殊情形最优次数的指数排版不清，需查原 PDF，不能据此重构公式。
原文摘要
Consider a randomization test in which an observed statistic is compared to a null distribution constructed by first drawing a random sample from the set of all possible permutations of the data and then calculating the statistic anew for each member of the random sample. If the power of such a test is investigated by simulation, the computer code must have two main loops. In the outer loop, which has O iterations, data are generated under a specific alternative hypothesis. For each outer iteration, there are I inner iterations in each of which the data are permuted and the statistic calculated. Assume that the costs of inner and outer iterations are known, and the total cost of the study is fixed, so that I and O are constrained by αO + IO = β for fixed (α, β). This article considers what the optimal choice for I is in a mean squared sense. A general expression is derived for the mean squared error of the distribution of p values. If the alternative hypothesis is close to the null, the optimal choice is the unique positive root of a fourth-degree polynomial. If, in addition, α = 0 (implying that the cost of generating a replicate is negligible compared to the cost of permuting the data and calculating a statistic) the optimal choice is Iopt = (4β)1/3.