On computationally efficient methods for testing multivariate distributions with unknown parameters

Sara Algeri Speaker
University of Minnesota
Monday, Aug 7: 2:25 PM - 2:45 PM
Topic-Contributed Paper Session 
Metro Toronto Convention Centre 
Despite the popularity of classical goodness fit tests such as Pearson's chi-squared and Kolmogorov-Smirnov, their applicability often faces serious challenges in practical applications. For instance, in a binned data regime, low counts may affect the validity of the asymptotic results. Excessively large bins, on the other hand, may lead to loss of power. In the unbinned data regime, tests such as Kolmogorov-Smirnov and Cramer-von Mises do not enjoy distribution-freeness if the models under study are multivariate and/or involve unknown parameters. As a result, one needs to simulate the distribution of the test statistic on a case-by-case basis. In this talk, I will discuss a testing strategy that allows us to overcome these shortcomings and equips experimentalists with a novel tool to perform goodness-of-fit while reducing substantially the computational costs.