Modelling Time-Varying Rankings with Autoregressive and Score-Driven Dynamics
Vladimír Holý, Jan Zouhar
发表信息：
Holý, V. & Zouhar, J. (2022). Modelling Time-Varying Rankings with Autoregressive and Score-Driven Dynamics. Journal of the Royal Statistical Society: Series C (Applied Statistics), 71(5), 1427-1450
We develop a new statistical model to analyse time-varying ranking data. The model can be used with a large number of ranked items, accommodates exogenous time-varying covariates and partial rankings, and is estimated via the maximum likelihood in a straightforward manner. Rankings are modelled using the Plackett-Luce distribution with time-varying worth parameters that follow a mean-reverting time series process. To capture the dependence of the worth parameters on past rankings, we utilise the conditional score in the fashion of the generalised autoregressive score (GAS) models. Simulation experiments show that the small-sample properties of the maximum-likelihood estimator improve rapidly with the length of the time series and suggest that statistical inference relying on conventional Hessian-based standard errors is usable even for medium-sized samples. In an empirical study, we apply the model to the results of the Ice Hockey World Championships. We also discuss applications to rankings based on underlying indices, repeated surveys, and non-parametric efficiency analysis.
Mixed spatial autoregressive (SAR) models with numerical covariates have been well studied. However, as non-numerical data, such as functional data and compositional data, receive substantial amounts of attention and are applied to economics, medicine and meteorology, it becomes necessary to develop flexible SAR models with multiple data types. In this article, we integrate three types of covariates, functional, compositional and numerical, in an SAR model. The new model has the merits of classical functional linear models and compositional linear models with scalar responses. Moreover, we dev…
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New York University（纽约大学）；Google AI（谷歌人工智能）；Facebook AI Research（脸书人工智能研究院）
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Southwestern University of Finance and Economics（西南财经大学）；The University of Sydney（悉尼大学）；McGill University（麦吉尔大学）；University of Waterloo（滑铁卢大学）；The London School of Economics and Political Science（伦敦政治经济学院）
University of North Carolina Charlotte（北卡罗来纳大学夏洛特分校）；University of Massachusetts Amherst（马萨诸塞大学阿默斯特分校）
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