Journal
BIOMETRICAL JOURNAL
Volume 65, Issue 2, Pages -Publisher
WILEY
DOI: 10.1002/bimj.202200073
Keywords
asymptotic power analysis; binomial Stein identity; count data; goodness-of-fit test; Stein-Chen identity
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This study derives the asymptotics of the Poisson and binomial Stein-type GoF statistics for general count distributions and investigates their performance and application in medical data.
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.
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