Allocation of Effort in Monte Carlo Simulation for Power of Permutation Tests
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置换检验功效模拟中的计算资源分配
- 研究问题
- 摘要研究固定计算预算下，如何在生成备择数据的外层重复与构造置换零分布的内层重复之间分配资源，以控制模拟误差。
- 方法与思路
- 作者将两层循环的成本纳入约束，推导 p 值分布估计的均方误差，并在备择接近原假设等情形下求解内层次数。
- 材料陈述的贡献
- 摘要给出一般均方误差表达式，并称近原假设时最优内层次数可由四次多项式确定；外层生成成本可忽略时还有简化结果。
- 阅读关注点
- 应核对优化所针对的误差对象、近原假设近似的条件，以及整数重复次数、实际运算成本与检验功效估计之间的关系。
- 阅读边界
- 摘要未提供完整推导和适用范围；简化结果的指数排版需查原文，不宜据此重构公式。索引未注明稿件版本或刊本变化。
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.