A New Approach to Tests and Confidence Bands for Distribution Functions
Speaker: Siddhaarth Sarkar
Abstract: This work introduces a new goodness-of-fit tests and corresponding confidence bands for distribution functions. The tests are inspired by multi-scale methods of testing and based on refined laws of the iterated logarithm for the normalized uniform empirical process. The goodness-of-fit tests perform well in signal detection problems involving sparsity, which they demonstrate under certain classical hypothesis testing frameworks. The confidence bands provided are also an improvement over Berk-Jones statistic and the DKW inequality confidence bands in the tail regions. I will be discussing an earlier version of the paper (version 2: https://arxiv.org/abs/1402.2918v2) and connect it to the generalisations the current draft proposes. I will cover a brief outline of prior work, the proposed statistic and confidence band method and it's optimality properties. If time permits, I will present a brief outline of the proof for the theorems related to confidence bands.