8 problems

Let $T_{n,m,p}^k$, $\tilde{T}_{n,m,p}^k$, and the studentized MDD statistic proposed by Yan and Zhang be the three studentized test statistics described above, with their respectiv…

Classifier-dependent estimation-quality conjecture. The observed differences in test performance between classifiers are due to the quality of their estimates of the classification…

The paper studies classification accuracy for two-sample mean testing of Gaussians with known covariance and also considers nonlinear settings. Unknown-covariance and nonlinear ext…

Consider kernelized nonlinear classification methods, including kernelized LDA, as extensions of the linear classification procedures studied in the paper. Kernelized classificatio…

Let the resubstitution classification-accuracy estimator be obtained by training LDA on all observations and evaluating it on those same observations. Resubstitution accuracy conje…

Let $X_1,\ldots,X_n$ and $Y_1,\ldots,Y_n$ be the two samples, and let $\widehat E^L$ be the leave-one-out classification-accuracy estimator obtained by training LDA after leaving o…

Weak-conditions conjecture. The conclusion that $R_3=o_P(U_{CQ}/\gamma^2)$ holds under much weaker conditions on $\gamma$, $n$, $\Sigma$, and $m$.

Gaussianity conjecture. The term $U_4$ is asymptotically Gaussian.