# Nonparametric depth-based methods for analyzing high-dimensional data. Applications to biomedical research

> **NIH NIH R21** · NORTHEASTERN UNIVERSITY · 2020 · $234,393

## Abstract

PROJECT SUMMARY
Technological development in many emerging research fields has provided us with large
collections of data of extraordinary complexity. Brain imaging technology, for example,
can generate complex collections of signals from individuals in different
neurophysiological states or clinical conditions. Developing new statistical tools to
analyze these rich data sets has become a limiting factor for the advancement of medical
diagnosis and biomedical research. The goal of this research proposal is to develop new
nonparametric and robust methods for analyzing general functional data with complicated
structure, such as images, using the idea of depth. In the last two decades there has been
an intensive development of notions of data depth, which have become powerful
nonparametric tools for analyzing multivariate and functional data. The methods proposed
in this project are based on a notion of data depth for general functions and the sample
rank-order it provides. Robust nonparametric statistics are particularly relevant in this
setting since usually few assumptions can be made about the data generating process
and potential outliers, which may be very difficult to detect, can affect the analysis in many
different ways. A taxonomy of the different possible types of outliers and
exploratory/visualization tools for detecting them will be developed. New approaches
based on novel envelope tests for checking if different groups of functions or images
come from the same distribution are proposed and will be studied. Recently, the PI has
started collaborating with investigators at New York State Psychiatric Institute, led by Dr.
Todd Ogden, on a data set that consists of positron emission tomography (PET) brain
images from a sample of individuals with major depressive disorders and a sample of
controls. The PI has also been working with Dr. Vidhu Thaker, a pediatrician at Columbia
University, on analyzing body mass index (BMI) trajectories of children with different
degrees of severe early childhood obesity. The methods introduced in this project will
extract from these data sets information of clinical relevance far beyond what has been
accomplished so far. In particular, the proposed depth-based nonparametric methods will
be used to: 1) rank a sample of functions from center-outwards, 2) identify outliers in the
data set and 3) develop nonparametric envelope tests for groups differences and identify
patterns. We believe that this work will boost the progress in different areas of
biomedicine.

## Key facts

- **NIH application ID:** 9998039
- **Project number:** 5R21MH120534-02
- **Recipient organization:** NORTHEASTERN UNIVERSITY
- **Principal Investigator:** Sara Lopez-Pintado
- **Activity code:** R21 (R01, R21, SBIR, etc.)
- **Funding institute:** NIH
- **Fiscal year:** 2020
- **Award amount:** $234,393
- **Award type:** 5
- **Project period:** 2019-08-16 → 2022-06-30

## Primary source

NIH RePORTER: https://reporter.nih.gov/project-details/9998039

## Citation

> US National Institutes of Health, RePORTER application 9998039, Nonparametric depth-based methods for analyzing high-dimensional data. Applications to biomedical research (5R21MH120534-02). Retrieved via AI Analytics 2026-07-06 from https://api.ai-analytics.org/grant/nih/9998039. Licensed CC0.

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