Optimal Stein-type goodness-of-fit tests for count data.

Autor: Weiß CH; Department of Mathematics and Statistics, Helmut Schmidt University, Hamburg, Germany., Puig P; Departament de Matemàtiques, Universitat Autònoma de Barcelona, Barcelona, Spain.; Centre de Recerca Matemàtica (CRM), Universitat Autònoma de Barcelona, Barcelona, Spain., Aleksandrov B; Department of Mathematics and Statistics, Helmut Schmidt University, Hamburg, Germany.
Jazyk: angličtina
Zdroj: Biometrical journal. Biometrische Zeitschrift [Biom J] 2023 Feb; Vol. 65 (2), pp. e2200073. Date of Electronic Publication: 2022 Sep 27.
DOI: 10.1002/bimj.202200073
Abstrakt: Common count distributions, such as the Poisson (binomial) distribution for unbounded (bounded) counts considered here, can be characterized by appropriate Stein identities. These identities, in turn, might be utilized to define a corresponding goodness-of-fit (GoF) test, the test statistic of which involves the computation of weighted means for a user-selected weight function f. Here, the choice of f should be done with respect to the relevant alternative scenario, as it will have great impact on the GoF-test's performance. We derive the asymptotics of both the Poisson and binomial Stein-type GoF-statistic for general count distributions (we also briefly consider the negative-binomial case), such that the asymptotic power is easily computed for arbitrary alternatives. This allows for an efficient implementation of optimal Stein tests, that is, which are most powerful within a given class  F $\mathcal {F}$ of weight functions. The performance and application of the optimal Stein-type GoF-tests is investigated by simulations and several medical data examples.
(© 2022 The Authors. Biometrical Journal published by Wiley-VCH GmbH.)
Databáze: MEDLINE
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