arXiv subjects

Siddhaarth Sarkar

Publications and source records attributed to Siddhaarth Sarkar.

3 recordsLinked to original sources

arXiv2026

Generalized Asymptotic Limit Theory and Inference for Isotonic Regression

Monotonicity is a natural shape constraint in nonparametric regression problems, arising for instance when predicting factory yield as a monotone function of labor hours. The widely used isotonic least squares estimator (LSE) does not require any tuning parameters and its rate of convergence and pointwise limiting distribution are well studied, assuming a specific local shape for the true monotone function. We introduce a general condition on the local behavior of this true function, uncovering a far richer family of asymptotic distributions than previously known. Valid inference in the classical framework has remained challenging due to the need to estimate nuisance parameters, and no existing methods address inference in our broader setup. We resolve this by showing the symmetry of these new limiting distributions, which allows the HulC procedure of Kuchibhotla, Balakrishnan, and Wasserman (2024) to produce asymptotically valid confidence intervals. More generally, our framework enables inference that remains uniformly valid over a suitably regular class of true functions.

math.ST↗

arXiv2025

Inference for quantile-parametrized families via CDF confidence bands

Quantile-based distribution families are an important subclass of parametric families, capable of exhibiting a wide range of behaviors using very few parameters. These parametric models present significant challenges for classical methods, since the CDF and density do not have a closed-form expression. Furthermore, approximate maximum likelihood estimation and related procedures may yield non-$\sqrt{n}$ and non-normal asymptotics over regions of the parameter space, making bootstrap and resampling techniques unreliable. We develop a novel inference framework that constructs confidence sets by inverting distribution-free confidence bands for the empirical CDF through the known quantile function. Our proposed inference procedure provides a principled and assumption-lean alternative in this setting, requiring no distributional assumptions beyond the parametric model specification and avoiding the computational and theoretical difficulties associated with likelihood-based methods for these complex parametric families. We demonstrate our framework on Tukey Lambda and generalized Lambda distributions, evaluate its performance through simulation studies, and illustrate its practical utility with an application to both a small-sample dataset (Twin Study) and a large-sample dataset (Spanish household incomes).

stat.ME↗

arXiv2023

Post-selection Inference for Conformal Prediction: Trading off Coverage for Precision

Conformal inference has played a pivotal role in providing uncertainty quantification for black-box ML prediction algorithms with finite sample guarantees. Traditionally, conformal prediction inference requires a data-independent specification of miscoverage level. In practical applications, one might want to update the miscoverage level after computing the prediction set. For example, in the context of binary classification, the analyst might start with a 95$\%$ prediction sets and see that most prediction sets contain all outcome classes. Prediction sets with both classes being undesirable, the analyst might desire to consider, say 80$\%$ prediction set. Construction of prediction sets that guarantee coverage with data-dependent miscoverage level can be considered as a post-selection inference problem. In this work, we develop simultaneous conformal inference to account for data-dependent miscoverage levels. Under the assumption of independent and identically distributed observations, our proposed methods have a finite sample simultaneous guarantee over all miscoverage levels. This allows practitioners to trade freely coverage probability for the quality of the prediction set by any criterion of their choice (say size of prediction set) while maintaining the finite sample guarantees similar to traditional conformal inference.

stat.ME↗