文章基本信息

标题：Generalized Rescaled Pólya urn and its statistical application
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作者：Giacomo Aletti ; Irene Crimaldi
期刊名称：Electronic Journal of Statistics
印刷版ISSN：1935-7524
出版年度：2022
卷号：16
期号：1
页码：1635-1680
DOI：10.1214/22-EJS1993
语种：English
出版社：Institute of Mathematical Statistics
摘要：We introduce the Generalized Rescaled Pólya (GRP) urn, that provides a generative model for a chi-squared test of goodness of fit for the long-term probabilities of clustered data, with independence between clusters and correlation, due to a reinforcement mechanism, inside each cluster. We apply the proposed test to a data set of Twitter posts about COVID-19 pandemic: in a few words, for a classical chi-squared test the data result strongly significant for the rejection of the null hypothesis (the daily long-run sentiment rate remains constant), but, taking into account the correlation among data, the introduced test leads to a different conclusion. Beside the statistical application, we point out that the GRP urn is a simple variant of the standard Eggenberger-Pólya urn, that, with suitable choices of the parameters, shows “local” reinforcement, almost sure convergence of the empirical mean to a deterministic limit and different asymptotic behaviours of the predictive mean. Moreover, the study of this model provides the opportunity to analyze stochastic approximation dynamics, that are unusual in the related literature.
关键词：60F05;60F15;62F03;62F05;62L20;central limit theorem;Chi-squared test;Pólya urn;reinforced stochastic process;reinforcement learning;stochastic approximation;urn model