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, advised by Professor S. N. Lahiri.

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*:

Does K-fold CV perform variable selection or does it lead to $\sqrt{n}$-consistency in Lasso?, with Mayukh Choudhury. Submitted.
Bootstrapping LASSO estimators under variable selection consistency in high dimensions and some higher order refinements, with A. Chatterjee and S. N. Lahiri. Under revision in Bernoulli.
Bootstrapping Lasso in Generalized Linear Models, with Mayukh Choudhury. Submitted.
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. 1-12. https://doi.org/10.1080/01621459.2024.2445873. (2025).
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.
Necessary and sufficient conditions for high dimensional Central Limit Theorems, with S. N. Lahiri.
A characterization of Gaussian distribution based on high dimensional Central Limit Theorem, with S. N. Lahiri.
Bootstrapping Sample Extremes, with D. Ghosh and 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.
High dimensional Stable laws, with Sayan Das.

* Please look into my research statement to know more about my research.

Teaching:

(A) At IIT Bombay:

Time Series Analysis (SI 509)**: Spring 2025, Spring 2022
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

* Undergraduate Courses ** Graduate Courses

Grants:

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)