Modern challenges in distribution testing

Hypothesis testing is one of the most classical problems in statistics. While it has enjoyed over a century of intense study, only recent focus has been on the small-sample regime, with interest in sample complexities and minimax rates. Our understanding of many fundamental problems is now quite mature, but there are several questions which have arisen over the last decade, which have not yet received adequate attention. The goal of this dissertation is to identify and address several contemporary challenges in distribution testing. In particular, we make progress in answering the following questions: ** Can we test distributions with tolerance to model misspecification? ** How does the complexity of distribution testing change as we consider different measures of distance? ** Can we efficiently test for membership in (potentially infinite) classes of distributions? ** How can we avoid the curse of dimensionality when testing multivariate distributions? ** Is it possible to perform hypothesis testing on sensitive data, while respecting privacy of the dataset? ** Can we design more efficient algorithms if the dataset is sampled actively? Directions for further investigation are also discussed.

Department dc:contributor.department

Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science.

Grantor dc:publisher

Massachusetts Institute of Technology

Year dc:date.issued

2018

Author dc:creator

• Kamath, Gautam (Gautam Chetan)

Advisor dc:contributor.advisor

• Constantinos Daskalakis.

• Electrical Engineering and Computer Science.

Statement dc:rights

• MIT theses are protected by copyright. They may be viewed, downloaded, or printed from this source but further reproduction or distribution in any format is prohibited without written permission.

Licence dc:rights.uri

• http://dspace.mit.edu/handle/1721.1/7582

Language dc:language.iso

eng

Handle dc:identifier.uri

http://hdl.handle.net/1721.1/120373

OAI identifier oai:identifier

oai:dspace.mit.edu:1721.1/120373