Thus with large n, we can hedge against the risk of model misspecification, while maintaining high statistical power if the model were actually a good fit to the data. This theoretical insight underpinning our methodology can be traced back to the works of L. Le Cam and E. Lehmann, among others.

Our tests are asymptotically as powerful as their parametric counterparts. The only difference is that our null is non-parametric, so it probably controls FDR. Even with large n, parametric tests can fail to control FDR when the model is misspecified.

Our method is especially well-suited for large-scale RNA-seq analysis. One might think that larger samples would allow the Central Limit Theorem to kick in, hence negating the advantage of non-parametric tests such as ours. Quite the opposite, in fact!