Inference for quantile-parametrized families via CDF confidence bands

Srijan Chattopadhyay, Siddhaarth Sarkar, Arun K. Kuchibhotla
Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence, PMLR 337:1034-1053, 2026.

Abstract

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 performance through simulation studies, and illustrate practical utility with applications to a small-sample dataset (Twin Study) and a large-sample dataset ({Spanish} household incomes).

Cite this Paper

BibTeX
@InProceedings{pmlr-v337-chattopadhyay26a, title = {Inference for quantile-parametrized families via CDF confidence bands}, author = {Chattopadhyay, Srijan and Sarkar, Siddhaarth and Kuchibhotla, Arun K.}, booktitle = {Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence}, pages = {1034--1053}, year = {2026}, editor = {Perković, Emilija and Malinsky, Daniel}, volume = {337}, series = {Proceedings of Machine Learning Research}, month = {17--21 Aug}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v337/main/assets/chattopadhyay26a/chattopadhyay26a.pdf}, url = {https://proceedings.mlr.press/v337/chattopadhyay26a.html}, abstract = {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 performance through simulation studies, and illustrate practical utility with applications to a small-sample dataset (Twin Study) and a large-sample dataset ({Spanish} household incomes).} }
Endnote
%0 Conference Paper %T Inference for quantile-parametrized families via CDF confidence bands %A Srijan Chattopadhyay %A Siddhaarth Sarkar %A Arun K. Kuchibhotla %B Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence %C Proceedings of Machine Learning Research %D 2026 %E Emilija Perković %E Daniel Malinsky %F pmlr-v337-chattopadhyay26a %I PMLR %P 1034--1053 %U https://proceedings.mlr.press/v337/chattopadhyay26a.html %V 337 %X 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 performance through simulation studies, and illustrate practical utility with applications to a small-sample dataset (Twin Study) and a large-sample dataset ({Spanish} household incomes).
APA
Chattopadhyay, S., Sarkar, S. & Kuchibhotla, A.K.. (2026). Inference for quantile-parametrized families via CDF confidence bands. Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence, in Proceedings of Machine Learning Research 337:1034-1053 Available from https://proceedings.mlr.press/v337/chattopadhyay26a.html.

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