Research Interests

Distributional Analysis and Inference

This area of my research develops statistical methods for analysing and comparing distributions, with applications to economic inequality, mobility, and related questions.

My contributions include methods for testing stochastic dominance and other distributional properties, with empirical likelihood providing an important information-theoretic foundation for several of these developments. I have also investigated robust statistical inference, including tests of distributional assumptions in regression models.

A recurring concern is understanding how missing observations, sample selection, and complex survey designs affect identification and statistical inference. This has motivated research combining distributional comparisons with missing data, partial identification, and design-based inference.

Information-Theoretic Methods and Optimal Transport

This area of my research investigates information-theoretic approaches to statistical inference and optimisation, alongside the mathematical, statistical, and computational foundations of optimal transport.

Information-theoretic methods feature in my work in distinct but related ways. Empirical likelihood provides a framework for statistical inference, particularly under inequality restrictions, while my research on information projections studies the existence, dual representation, and approximation of solutions to constrained Kullback–Leibler minimisation problems.

More recently, I have investigated the statistical estimation and computation of entropic optimal transport, as well as the use of optimal transport to study distributional relationships, partial identification, and classical problems in statistical inference.

These two broad research interests overlap through their shared concerns with distributions, statistical inference, and optimisation under constraints. At the same time, each motivates mathematical and statistical questions of independent interest.

Selected Research Contributions

My research contributions include:

• Stochastic dominance and distributional inference: Developing statistical procedures for testing distributional orderings, including empirical likelihood methods and inference under missing observations and complex survey designs.

• Empirical likelihood and inequality constraints: Developing empirical likelihood-based inference methods for testing inequality restrictions on statistical functionals.

• Economic inequality and robust statistical inference: Investigating tests for health inequality and robust tests of distributional assumptions in linear regression models.

• Information projections: Establishing existence, dual representations, and approximation results for Kullback–Leibler information projections under moment inequality constraints.

• Statistical optimal transport: Developing statistical estimation and computational methods for entropic optimal transport, including sieve-based approaches.

• Partial identification with incomplete observations: Deriving sharp Fréchet–Hoeffding bounds under selectively incomplete observation using optimal transport and finite-dimensional optimisation.

• Geometric perspectives on statistical inference: Investigating optimal transport interpretations of foundational statistical results, including the Neyman–Pearson lemma.

A complete list of published articles and working papers is available on my Publications & Working Papers page.

Current Research Directions

My ongoing research focuses on distributional inference with incomplete data, the mathematical and computational foundations of statistical optimal transport, and the use of optimal transport and information-theoretic methods to investigate fundamental problems in statistical inference.

An important objective across these projects is to develop methods that combine mathematical rigour with computational tractability and practical relevance.