标题： 高维数据下欧几里得距离判别规则的误分类误差的渐近性质 显示英文标题

标题： Asymptotic Properties of the Misclassification Errors for Euclidean Distance Discriminant Rule in High-Dimensional Data

摘要： 欧几里得距离判别规则（EDDR）的性能精度在高维渐近框架下进行了研究，该框架允许维度超过样本数量。 在协方差矩阵迹线的温和假设下，我们得到的新结果提供了条件误分类误差的渐近分布和期望误分类误差的一致且渐近无偏估计式的显式表达。 为了获得这些性质，建立了关于二次型和Wishart矩阵高次幂迹线的渐近正态性新结果。 利用我们的渐近结果，我们进一步发展了两种确定EDDR截断点的通用方法以调整误分类误差。 最后，我们在有限样本应用中通过数值验证了我们渐近发现的高准确性以及截断确定方法，包括大样本和高维场景。 显示英文摘要

摘要： Performance accuracy of the Euclidean Distance Discriminant rule (EDDR) is studied in the high-dimensional asymptotic framework which allows the dimensionality to exceed sample size. Under mild assumptions on the traces of the covariance matrix, our new results provide the asymptotic distribution of the conditional misclassification error and the explicit expression for the consistent and asymptotically unbiased estimator of the expected misclassification error. To get these properties, new results on the asymptotic normality of the quadratic forms and traces of the higher power of Wishart matrix, are established. Using our asymptotic results, we further develop two generic methods of determining a cut-off point for EDDR to adjust the misclassification errors. Finally, we numerically justify the high accuracy of our asymptotic findings along with the cut-off determination methods in finite sample applications, inclusive of the large sample and high-dimensional scenarios.