Contributed Poster Presentations: IMS

In this work we propose a class of goodness-of-fit tests for testing if the marginal distribution of a vector of pairwise distances follows a specified distribution or family of distributions. These tests are used in forensic science for deciding if a certain known-source distribution is reasonable for deciding if an object arose from a specified source. Forensic science consists of many few-shot learning problems, where there are few objects per source, with a large number of sources. This class of tests is designed to deal with the small sample sizes per source (class), and the dependency arising from the pairwise comparisons.

Unlike in standard goodness-of-fit tests with a fixed distribution, there is one free parameter that accounts for the dependencies between the pairwise comparisons. We will focus on strategies for estimating this nuisance parameter and the effect that different estimation strategies (REML, super efficient MLE, where sample size n acts as n-choose-2) have on the resulting Type 1 and Type 2 errors, using Monte Carlo simulation. We will also look at the theoretical differences of the estimation strategies for this goodness-of-fit test. 

The low-tubal-rank tensor model has been used for real-world multidimensional data to capture signals in the frequency domain. Algorithms have been developed to estimate low-rank third-order tensors from partial and corrupted entries. However, uncertainty quantification and statistical inference for these estimates remain largely unclear.

Our work addresses this gap. We introduce a flexible framework for making inferences about general linear forms of a large tensor whenever an entry-wise consistent estimator is available. Under mild regularity conditions, we construct asymptotically normal estimators of these linear forms through double-sample debiasing and low-rank projection. These estimators allow us to construct confidence intervals and perform hypothesis testing. Simulation studies support our theoretical results, and we apply the method to the total electron content (TEC) reconstruction problem.