Debraj Das

I am an Assistant Professor in the Department of Mathematics at Indian Institute of Technology Bombay. Before joining IIT Bombay, I was an Assistant Professor in the Department of Mathematics and Statistics at IIT Kanpur. Prior to that I was an Inspire Faculty at Indian Statistical Institute, Delhi Center and a Visiting Assistant Professor at Department of Statistics, University of Wisconsin-Madison. I completed my PhD in Statistics from North Carolina State University.

Research Interests:

Asymptotic Theory of Statistics
Rates of Convergence to CLT, Edgeworth Expansions
Bootstrap, Empirical Likelihoods
Time Series
Statistical Analysis of Networks

Research Papers:

(A) Published/Completed*:

Asymptotic theory of K-fold CV in Lasso and the validity of Bootstrap, with Mayukh Choudhury. Submitted. Available at Arxiv.
Necessary and sufficient conditions for high dimensional Central Limit Theorems, with S. N. Lahiri. Submitted. Available at Arxiv.
Bootstrapping Lasso in Generalized Linear Models, with Mayukh Choudhury. Submitted. Available at Arxiv.
Bootstrapping Lasso estimators under variable selection consistency in high dimensions and some higher order refinements, with A. Chatterjee and S. N. Lahiri. To appear in Bernoulli. Available at Arxiv.
PEBBLE: A Second Order Correct Bootstrap method in Logistic Regression, with P. Das. Bernoulli, 31 (4), 2814-2837. (2025). Available at Arxiv.
Higher Order Accurate Symmetric Bootstrap Confidence Intervals in High Dimensional Penalized Regression, with A. Chatterjee and S. N. Lahiri. Journal of the American Statistical Association. 120 (551), 1645-1656. (2025). Available at Arxiv.
Central Limit Theorem and near classical Berry-Esseen rate for self normalized sums in high dimensions. Bernoulli, 30 (1), 278-303. (2024). Available at Arxiv.
Central Limit Theorem in High Dimensions: Optimal Bounds on dimension growth rate, with S. N. Lahiri. Transactions of the American Mathematical Society, 374 (10), 6991-7009. (2021). Available at Arxiv.
Distributional Consistency of Lasso by Perturbation Bootstrap, with S. N. Lahiri. Biometrika, 106(4), 957-964. (2019). Available at Arxiv.
Perturbation Bootstrap in Adaptive LASSO, with K. Gregory and S. N. Lahiri. Annals of Statistics, 47, 2080-2116. (2019). Available at Arxiv.
Second Order Correctness of Perturbation Bootstrap M-Estimator of Multiple Linear Regression Parameter, with S. N. Lahiri. Bernoulli, 25(1), 654-682. (2019). Available at Arxiv.
Estimation of Total Fusion Reactivity and Contribution from Supra thermal Tail using 3-parameter Dagum Ion Speed Distribution,With R. Majumdar. Ann. Nucl. Energy, 97, 66-75. (2016). Available at Arxiv.

(B) Ongoing*:

High dimensional mean testing using Logistic Regression, with Sayan Das and Subhajit Dutta.
High dimensional inference in Generalized Linear Models, with Mayukh Choudhury.
A characterization of Gaussian distribution based on high dimensional Central Limit Theorem, with S. N. Lahiri.
Choudhury, M., Das, D. and Ghosh, S. Asymptotic theory of tail dependence measure for Checkerboard Copula, with Mayukh Choudhury and Sujit Ghosh.
Bootstrapping Sample Extremes, with D. Ghosh and S. N. Lahiri.
Low rank matrix estimation in linear models, with Arindam Chatterjee and Mayukh Choudhury.
High dimensional Stable laws, with Sayan Das.
Tail dependence measures based on Chatterjee's correlation, with Mayukh Choudhury and Sujit Ghosh.

Teaching:

(A) At IIT Bombay:

Time Series Analysis (SI 509): Spring 2026, Spring 2025, Spring 2022
Multivariate Analysis (SI 5055): Fall 2025
Probability I (SI 427): Fall 2021
Statistical Inference II (SI 546): Spring 2024
Random Graphs (SI 539): Spring 2024
Statistical Inference I (SI 424): Fall 2024, Fall 2023, Spring 2023, Fall 2022, Spring 2021

(B) At IIT Kanpur:

Inference I (MTH 418): Spring 2020
Probability Theory (MTH 754): Fall 2020 and Fall 2019

Statistical Methods for Bio-science I (Stat 571) : Fall 2017
Introductory Statistics for Engineers (Stat 324) : Spring 2018 and Fall 2017

Grants:

ANRF MATRICS grant: 2026 - 2030.
European Union funding in the Team Finland Knowledge (TFK) Program: 2025 - 2027. (jointly with Dr. Sangita Kulathinal, Dr. Koushik Saha, Dr. Siuli Mukhopadhyay, Dr. Souvik Banerjee and Dr. Asha Kamath )
DST INSPIRE Grant: 2019 - 2024
SERB MATRICS Grant on COVID-19: 2020 - 2021 (jointly with Dr. Subhajit Dutta, Dr. Minerva Mukhopadhyay and Dr. Hamim Zafar)