6 problems

Let $X_i$ denote the covariate vector for unit $i$, and suppose Assumption(1) currently requires $X_i$ to be uniformly bounded. Covariate-tail relaxation conjecture. It should be p…

Let $\nu^{\mathsf{rd}}$, $\nu^{\mathsf{rd}\dag}$, and $\mathsf{var}(\widehat{\tau}_{\mathsf{unadj}})$ denote the variance quantities defined in the paper for the covariate-adjusted…

The type-I error rate conjecture. The type-I error rate under rerandomization should not exceed that under complete randomization:

Consider the reversed two-stage procedure in which eligible units are first matched into groups of size $k'$, their centroids are then matched into homogeneous groups of size $k$,…

Regression–weighting equivalence conjecture. The equivalence between regression and weighting also holds even with missing covariates.

Let an experimental design assign treatment indicators with possibly non-uniform first-order probabilities, so that $\boldsymbol{z}$ is not required to satisfy $ui=frac{1}{2}$ for…