A UNIFIED ANALYSIS OF LIKELIHOOD-BASED ESTIMATORS IN THE PLACKETT–LUCE MODEL

Ruijian Han; Yiming Xu

doi:10.1214/25-AOS2530

A UNIFIED ANALYSIS OF LIKELIHOOD-BASED ESTIMATORS IN THE PLACKETT–LUCE MODEL

Ruijian Han
, Yiming Xu

Mathematics

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

The Plackett–Luce model has been extensively used for rank aggregation in social choice theory. A central statistical question in this model concerns estimating the utility vector that governs the model’s likelihood. In this paper, we investigate the asymptotic theory of utility vector estimation by maximizing different types of likelihood, such as full, marginal, and quasi-likelihood. Starting from interpreting the estimating equations of these estimators to gain some initial insights, we analyze their asymptotic behavior as the number of compared objects increases. In particular, we establish both uniform consistency and asymptotic normality of these estimators and discuss the trade-off between statistical efficiency and computational complexity. For generality, our results are proven for deterministic graph sequences under appropriate graph topology conditions. These conditions are shown to be informative when applied to common sampling scenarios, such as nonuniform random hypergraph models and hypergraph stochastic block models. Numerical results are provided to support our findings.

Original language	English
Pages (from-to)	2077-2102
Number of pages	26
Journal	Annals of Statistics
Volume	53
Issue number	5
DOIs	https://doi.org/10.1214/25-AOS2530
State	Published - Oct 2025

Bibliographical note

Publisher Copyright:
© Institute of Mathematical Statistics, 2025.

Funding

Y. Xu was partially supported by the University of Kentucky for the start-up funding and the AMS-Simons Travel grant (No. 3048116562). Funding. R. Han was partially supported by the Hong Kong Research Grants Council General Research Fund (No. 14301821) and the Hong Kong Polytechnic University (P0044617, P0045351). R. Han was partially supported by the Hong Kong Research Grants Council General Research Fund (No. 14301821) and the Hong Kong Polytechnic University (P0044617, P0045351). Y. Xu was partially supported by the University of Kentucky for the start-up funding and the AMS-Simons Travel grant (No. 3048116562).

Funders	Funder number
3048116562
Research Grants Council, University Grants Committee	14301821
Hong Kong Polytechnic University	P0045351, P0044617

Keywords

Asymptotic normality
entrywise error
hypergraph
likelihood-based estimation
Plackett–Luce model

ASJC Scopus subject areas

Statistics and Probability
Statistics, Probability and Uncertainty

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10.1214/25-AOS2530

Cite this

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title = "A UNIFIED ANALYSIS OF LIKELIHOOD-BASED ESTIMATORS IN THE PLACKETT–LUCE MODEL",

abstract = "The Plackett–Luce model has been extensively used for rank aggregation in social choice theory. A central statistical question in this model concerns estimating the utility vector that governs the model{\textquoteright}s likelihood. In this paper, we investigate the asymptotic theory of utility vector estimation by maximizing different types of likelihood, such as full, marginal, and quasi-likelihood. Starting from interpreting the estimating equations of these estimators to gain some initial insights, we analyze their asymptotic behavior as the number of compared objects increases. In particular, we establish both uniform consistency and asymptotic normality of these estimators and discuss the trade-off between statistical efficiency and computational complexity. For generality, our results are proven for deterministic graph sequences under appropriate graph topology conditions. These conditions are shown to be informative when applied to common sampling scenarios, such as nonuniform random hypergraph models and hypergraph stochastic block models. Numerical results are provided to support our findings.",

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PY - 2025/10

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N2 - The Plackett–Luce model has been extensively used for rank aggregation in social choice theory. A central statistical question in this model concerns estimating the utility vector that governs the model’s likelihood. In this paper, we investigate the asymptotic theory of utility vector estimation by maximizing different types of likelihood, such as full, marginal, and quasi-likelihood. Starting from interpreting the estimating equations of these estimators to gain some initial insights, we analyze their asymptotic behavior as the number of compared objects increases. In particular, we establish both uniform consistency and asymptotic normality of these estimators and discuss the trade-off between statistical efficiency and computational complexity. For generality, our results are proven for deterministic graph sequences under appropriate graph topology conditions. These conditions are shown to be informative when applied to common sampling scenarios, such as nonuniform random hypergraph models and hypergraph stochastic block models. Numerical results are provided to support our findings.

AB - The Plackett–Luce model has been extensively used for rank aggregation in social choice theory. A central statistical question in this model concerns estimating the utility vector that governs the model’s likelihood. In this paper, we investigate the asymptotic theory of utility vector estimation by maximizing different types of likelihood, such as full, marginal, and quasi-likelihood. Starting from interpreting the estimating equations of these estimators to gain some initial insights, we analyze their asymptotic behavior as the number of compared objects increases. In particular, we establish both uniform consistency and asymptotic normality of these estimators and discuss the trade-off between statistical efficiency and computational complexity. For generality, our results are proven for deterministic graph sequences under appropriate graph topology conditions. These conditions are shown to be informative when applied to common sampling scenarios, such as nonuniform random hypergraph models and hypergraph stochastic block models. Numerical results are provided to support our findings.

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A UNIFIED ANALYSIS OF LIKELIHOOD-BASED ESTIMATORS IN THE PLACKETT–LUCE MODEL

Abstract

Bibliographical note

Funding

Keywords

ASJC Scopus subject areas

Access to Document

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