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Bibliographic Details
Main Authors: Osom, Albert, Shojaie, Ali, Hudson, Aaron
Format: Preprint
Published: 2026
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Online Access:https://arxiv.org/abs/2604.20045
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author Osom, Albert
Shojaie, Ali
Hudson, Aaron
author_facet Osom, Albert
Shojaie, Ali
Hudson, Aaron
contents We present a general nonparametric approach for testing whether a statistical parameter defined through conditional distributions is constant across the conditioning variables. Such hypotheses arise naturally in problems such as assessing treatment effect heterogeneity, conditional associational effects, and conditional mean dependence. Our framework studies function-valued parameters obtained by evaluating a smooth statistical functional on conditional probability distributions. We establish an explicit connection between our test and procedures based on studying the norm of the function-valued parameter. Unlike many existing norm-based tests, which exhibit poor asymptotic behavior under the null, the proposed test statistic admits a tractable limiting null distribution. We illustrate the applicability of the proposed test through several examples, assess its operating characteristics in simulation studies, and apply it to data from a breast cancer trial to identify predictive biomarkers for response to adjuvant chemotherapy.
format Preprint
id arxiv_https___arxiv_org_abs_2604_20045
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle A general nonparametric framework for testing hypotheses about function-valued parameters
Osom, Albert
Shojaie, Ali
Hudson, Aaron
Methodology
We present a general nonparametric approach for testing whether a statistical parameter defined through conditional distributions is constant across the conditioning variables. Such hypotheses arise naturally in problems such as assessing treatment effect heterogeneity, conditional associational effects, and conditional mean dependence. Our framework studies function-valued parameters obtained by evaluating a smooth statistical functional on conditional probability distributions. We establish an explicit connection between our test and procedures based on studying the norm of the function-valued parameter. Unlike many existing norm-based tests, which exhibit poor asymptotic behavior under the null, the proposed test statistic admits a tractable limiting null distribution. We illustrate the applicability of the proposed test through several examples, assess its operating characteristics in simulation studies, and apply it to data from a breast cancer trial to identify predictive biomarkers for response to adjuvant chemotherapy.
title A general nonparametric framework for testing hypotheses about function-valued parameters
topic Methodology
url https://arxiv.org/abs/2604.20045