Abstract

Statistical inference in parametric models (e.g., the Bradley–Terry

model and its variants) for paired-comparison data has been explored in the

high-dimensional regime, in which the number of items involving in paired comparisons diverges. However, parametric models are highly susceptible to model

misspecification. To relax the assumption of known distributions and provide

flexibility, we propose a semiparametric framework for modeling the merits of

items and covariate effects (e.g., home-field advantage) by introducing latent

random variables with unspecified distributions. As the number of parameters

increases with the number of items, semiparametric inference is highly nontrivial. To address this issue, we employ a kernel-based least squares approach to

estimate all unknown parameters. When each pair of items has a fixed number of

comparisons and the number of items tends to infinity, we prove the consistency

of all resulting estimators and derive their asymptotic normal distributions. To

the best of our knowledge, this is the first study to conduct a semiparametric

analysis of paired comparisons with an increasing dimension. We conduct simulations to evaluate the finite-sample performance of the proposed method and

illustrate its practical utility by analyzing an NBA dataset.

Key words and phrases: Asymptotic normality, Consistency, Covariate effects, Paired comparison, Semiparametric model

Information

Preprint No.SS-2025-0318
Manuscript IDSS-2025-0318
Complete AuthorsHaoyue Song, Lianqiang Qu, Ting Yan, Yuguo Chen
Corresponding AuthorsTing Yan
Emailstingyanty@mail.ccnu.edu.cn

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Acknowledgments

We are very grateful to three referees, the associated editor, and the editor

for their valuable comments that have greatly improved the manuscript.

Yan is supported by the National Natural Science Foundation of China

(No. 12171188, 12322114).

Supplementary Materials

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5.

Summary

We have proposed a semiparametric paired comparison model that incorporates covariates. By introducing a special regressor, we developed a kernel-

based least squares method to estimate all unknown parameters in the

Supplementary materials are available for download.