NSF Org:	DMS Division Of Mathematical Sciences
Recipient:	THE TRUSTEES OF COLUMBIA UNIVERSITY IN THE CITY OF NEW YORK
Initial Amendment Date:	June 12, 2023
Latest Amendment Date:	June 12, 2023
Award Number:	2311062
Award Instrument:	Standard Grant
Program Manager:	Yong Zeng yzeng@nsf.gov  (703)292-7299 DMS  Division Of Mathematical Sciences MPS  Directorate for Mathematical and Physical Sciences
Start Date:	July 1, 2023
End Date:	June 30, 2026 (Estimated)
Total Intended Award Amount:	$300,000.00
Total Awarded Amount to Date:	$300,000.00
Funds Obligated to Date:	FY 2023 = $300,000.00
History of Investigator:	Bodhisattva Sen (Principal Investigator) bodhi@stat.columbia.edu
Recipient Sponsored Research Office:	Columbia University 615 W 131ST ST NEW YORK NY  US  10027-7922 (212)854-6851
Sponsor Congressional District:	13
Primary Place of Performance:	Columbia University 202 LOW LIBRARY 535 W 116 ST MC 4309, NEW YORK NY  US  10027
Primary Place of Performance Congressional District:	13
Unique Entity Identifier (UEI):	F4N1QNPB95M4
Parent UEI:
NSF Program(s):	STATISTICS
Primary Program Source:	01002324DB NSF RESEARCH & RELATED ACTIVIT
Program Reference Code(s):	079Z
Program Element Code(s):	126900
Award Agency Code:	4900
Fund Agency Code:	4900
Assistance Listing Number(s):	47.049

ABSTRACT

Statistical hypothesis testing is the formal setup a statistician employs to decide between two competing hypotheses about the underlying data generating mechanism. Nonparametric methods have become increasingly popular in the theory and practice of statistics in recent times, primarily because of the greater flexibility they offer over parametric models. This research project investigates some problems in nonparametric hypothesis testing for multi-dimensional data. Modern computational capabilities, and the expanded data sets produced by modern scientific equipment have greatly increased the scope of such flexible statistical inference procedures. The investigator will develop a framework for "distribution-free" inference with multivariate data that generalizes many well-known and popular statistical ideas used for analyzing univariate data. On the collaborative front, the investigator will continue interdisciplinary research in astronomy. Further, some of these research problems will form the dissertation thesis of a current PhD student at Columbia. The investigator also plans to continue the tradition of mentoring undergraduate summer interns.

The main thrust of this research is to study distribution-free methods for multivariate and Hilbert space-valued data, based on the theory of optimal transport -- a branch of mathematics that has received much attention lately in applied mathematics/probability/machine learning. These methods generalize the classical univariate rank-based methods to multivariate data. In the second part of the proposal, the investigator will study the asymptotic relative efficiency (ARE) of nonparametric tests and provide a characterization of ARE when the underlying test statistics converge weakly to an infinite mixtures of chi-square distributions, under the null hypothesis. This framework includes many interesting examples that arise in practice, including two-sample testing, independence testing, testing multivariate symmetry, inference on directional data, etc. The investigator will also develop a theoretical framework for estimating the ARE in this setting.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

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