10 Performance Guaranteed Confidence Sets of Ranks

Oregon Convention Center 

Ranks of institutes are often estimated based on estimates of certain latent features of the institutes,  and due to sample randomness it is of interest to quantify the uncertainty associated with the estimated ranks. This task is especially important in often-seen ``near tie'' situations in which the estimated latent features are not well separated among some of the institutes resulting in a nonignorable portion of wrongly ordered estimated ranks. Uncertainty quantification can help mitigate some of the issues and give us a fuller picture, but the task is very challenging  because the ranks are discrete parameters and the standard inference methods developed under regularity conditions do not apply. Bayesian methods are sensitive to prior choices while large sample-based methods do not work since the central limit theorem fail to hold for the estimated ranks. In this article, we propose a repro Samples Method to address this nontrivial irregular inference problem by developing a confidence set for the true rank of the institutes. The confidence set obtained has finite sample coverage guarantee and the method can handle difficult near tie cases. The effectiveness of the proposed de

Inference on discrete parameter space

Finite-sample performance guarantee

Discrete parameter space

irregular inference problem