A0717
Title: Adaptive robust confidence intervals: Location models and networks
Authors: Yuetian Luo - Rutgers University (United States) [presenting]
Chao Gao - University of Chicago (United States)
Abstract: The purpose is to study the construction of confidence intervals under Huber's contamination model. When the contamination proportion is unknown, the necessary adaptation cost of the problem is characterized. In particular, for the Gaussian location model, the optimal length of an adaptive confidence interval is proved to be exponentially wider than that of a non-adaptive one. Results for general location models will be discussed. In addition, the same problem is also considered in a network setting for an Erdos-Renyi graph with node contamination. It is shown that the hardness of the adaptive confidence interval construction is implied by the detection threshold between the Erdos-Renyi model and the stochastic block model.
