2020/09/10 by Chiang, Harold D., Kato, Kengo, Sasaki, Yuya · 1 citation
#Econometrics (econ.EM) #FOS: Economics and business #FOS: Mathematics #Statistics Theory (math.ST)
paper · doi:10.48550/arxiv.2009.05150
We consider inference for high-dimensional separately and jointly exchangeable arrays where the dimensions may be much larger than the sample sizes. For both exchangeable arrays, we first derive high-dimensional central limit theorems over the rectangles and subsequently develop novel multiplier bootstraps with theoretical guarantees. These theoretical results rely on new technical tools such as Hoeffding-type decomposition and maximal inequalities for the degenerate components in the Hoeffiding-type decomposition for the exchangeable arrays. We exhibit applications of our methods to uniform confidence bands for density estimation under joint exchangeability and penalty choice for ℓ1-penalized regression under separate exchangeability. Extensive simulations demonstrate precise uniform coverage rates. We illustrate by constructing uniform confidence bands for international trade network densities.