Higher-Order Asymptotic Normality of Approximations to the Modified Signed Likelihood Ratio Statistic for Regular Models

Approximations to the modified signed likelihood ratio statistic are asymptotically standard normal with error of order n⁻¹, where n is the sample size. Proofs of this fact generally require that the sufficient statistic of the model be written as ($\hat{\theta}$, a), where $\hat{\theta}$ is the max...

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Bibliographische Detailangaben
Veröffentlicht in:The Annals of Statistics. - Institute of Mathematical Statistics. - 35(2007), 5, Seite 2054-2074
1. Verfasser: He, Heping (VerfasserIn)
Weitere Verfasser: Severini, Thomas A.
Format: Online-Aufsatz
Sprache:English
Veröffentlicht: 2007
Zugriff auf das übergeordnete Werk:The Annals of Statistics
Schlagworte:Edgeworth expansion theory Modified signed likelihood ratio statistic Higher-order normality Sufficient statistic Cramér-Edgeworth polynomial Mathematics Behavioral sciences
Beschreibung
Zusammenfassung:Approximations to the modified signed likelihood ratio statistic are asymptotically standard normal with error of order n⁻¹, where n is the sample size. Proofs of this fact generally require that the sufficient statistic of the model be written as ($\hat{\theta}$, a), where $\hat{\theta}$ is the maximum likelihood estimator of the parameter θ of the model and a is an ancillary statistic. This condition is very difficult or impossible to verify for many models. However, calculation of the statistics themselves does not require this condition. The goal of this paper is to provide conditions under which these statistics are asymptotically normally distributed to order n⁻¹ without making any assumption about the sufficient statistic of the model.
ISSN:00905364