Efficient selection of the best system: Indifference-zone-free procedures with multi-dimensional Brownian motion
提出一种无需无差异区间参数的全序贯选择方法，利用多维布朗运动的贝塞尔过程性质简化统计保证推导，在已知等方差和未知不等方差情形下均适用，数值实验表明该方法能减少保守性并提高样本效率。
The limitations of traditional indifference-zone (IZ) ranking and selection procedures stem from their reliance on an IZ parameter, which is often unknown in practice and can lead to inefficiencies. Additionally, since exact evaluation of the probability of correct selection (PCS) is generally unattainable, these approaches commonly rely on a Bonferroni-Inequality-type lower bound to ensure the worst-case PCS, which introduces further conservativeness. To overcome these challenges, we propose fully sequential IZ-free procedures that eliminate the need for an IZ parameter and reduce the conservativeness associated with Bonferroni Inequality approaches. We demonstrate that, in the context of IZ-free procedures, the screening statistic corresponds to the Euclidean distance of a multi-dimensional standard Brownian motion, which behaves as a Bessel process. This connection simplifies the derivation of statistical guarantees for the proposed procedures and facilitates the analytical expressions for key parameters. Our procedures accommodate both known equal variances and unknown unequal variances, with statistical guarantees established in the known equal variance case. Numerical experiments confirm that the proposed procedures outperform existing methods in reducing PCS conservativeness and improving sample size efficiency. These advancements enhance the robustness and practicality of IZ-free procedures for diverse applications.