Score Statistics for Current Status Data: Comparisons with Likelihood Ratio and Wald Statistics

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Score Statistics for Current Status Data: Comparisons with Likelihood Ratio and Wald Statistics

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dc.contributor.author Wellner, Jon A. en_US
dc.contributor.author Banerjee, Moulinath en_US
dc.date.accessioned 2009-12-15T21:11:21Z
dc.date.available 2009-12-15T21:11:21Z
dc.date.issued 2005 en_US
dc.identifier.citation Score Statistics for Current Status Data: Comparisons with Likelihood Ratio and Wald Statistics," The International Journal of Biostatistics: Vol. 1 : Iss. 1, Article 3. en_US
dc.identifier.other 10.2202/1557-4679.1001 en_US
dc.identifier.uri http://www.bepress.com/ijb/vol1/iss1/3 en_US
dc.identifier.uri http://hdl.handle.net/1773/15540
dc.description en_US
dc.description.abstract In this paper we introduce three natural "score statistics" for testing the hypothesis that F(t_0)takes on a fixed value in the context of nonparametric inference with current status data. These three new test statistics have natural interpretations in terms of certain (weighted) L_2 distances, and are also connected to natural "one-sided" scores. We compare these new test statistics with the analogue of the classical Wald statistic and the likelihood ratio statistic introduced in Banerjee and Wellner (2001) for the same testing problem. Under classical "regular" statistical problems the likelihood ratio, score, and Wald statistics all have the same chi-squared limiting distribution under the null hypothesis. In sharp contrast, in this non-regular problem all three statistics have different limiting distributions under the null hypothesis. Thus we begin by establishing the limit distribution theory of the statistics under the null hypothesis, and discuss calculation of the relevant critical points for the test statistics. Once the null distribution theory is known, the immediate question becomes that of power. We establish the limiting behavior of the three types of statistics under local alternatives. We have also compared the power of these five different statistics via a limited Monte-Carlo study. Our conclusions are: (a) the Wald statistic is less powerful than the likelihood ratio and score statistics; and (b) one of the score statistics may have more power than the likelihood ratio statistic for some alternatives. en_US
dc.description.sponsorship NSF, NIAID en_US
dc.language.iso en_US en_US
dc.rights Copyright held by the authors en_US
dc.subject en_US
dc.subject en_US
dc.subject en_US
dc.subject en_US
dc.title Score Statistics for Current Status Data: Comparisons with Likelihood Ratio and Wald Statistics en_US
dc.type Article en_US


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