When data analysts train a classifier and check if its accuracy is significantly different from random guessing, they are implicitly and indirectly performing a hypothesis test (two sample testing) and it is of importance to ask whether this indirect method for testing is statistically optimal or not. Given that hypothesis tests attempt to maximize statistical power subject to a bound on the allowable false positive rate, while prediction attempts to minimize statistical risk on future predictions on unseen data, we wish to study whether a predictive approach for an ultimate aim of testing is prudent. We formalize this problem by considering the two-sample mean-testing setting where one must determine if the means of two Gaussians (with known and equal covariance) are the same or not, but the analyst indirectly does so by checking whether the accuracy achieved by Fisher's LDA classifier is significantly different from chance or not. Unexpectedly, we find that the asymptotic power of LDA's sample-splitting classification accuracy is actually minimax rate-optimal in terms of problem-dependent parameters. Since prediction is commonly thought to be harder than testing, it might come as a surprise to some that solving a harder problem does not create a information-theoretic bottleneck for the easier one. On the flip side, even though the power is rate-optimal, our derivation suggests that it may be worse by a small constant factor; hence practitioners must be wary of using (admittedly flexible) prediction methods on disguised testing problems.

探究在高维情况下对分类器的精度验证，证明一种基于排列组合的测试方法具有连续性及德克斯特拉极限分布的高斯近似测试也具有连续性，并以高斯分布为例进一步研究了线性判别分析和 Hotelling's 测试等方法的功率。

作为双样本检验代理的分类准确性