Research
You can also find my articles on my Google Scholar profile.
Current projects
- Unified Inference framework for functionals: Assumption-flexible with Post-Selection Guarantees
- Developing methods for deriving confidence intervals for various functionals (e.g., mean or median) under user-specified assumptions (e.g., finite variance or tail behavior), using confidence sets for CDFs.
- This offers a flexible inference strategy that reduces dependence on strict assumptions and enhances applicability across diverse contexts.
- Inference for quantile-parametrized distributions
- Quantile-based distributions are flexible and widely applicable, but lack closed-form densities, making standard inference challenging.
- Classical methods like MLE can yield non-$\sqrt{n}$ and non-normal asymptotic behavior in certain parameter regions, making bootstrap and resampling techniques unreliable.
- We develop a new inference framework tailored to parametric models defined via the quantile function, offering principled and assumption-lean alternatives for inference.
- Random forests and decision trees
- Focusing on density estimation trees (DETs), a data-driven partitioning approach for tree-structured density estimation.
- Establishing the necessary conditions for DETs to be consistent estimators, under different metrics such as \(L^2\) norm or KL divergence.
- Exploring methods to quantify uncertainty in density estimates from DETs, enhancing their reliability and interpretability in machine learning applications.