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

Banerjee Moulinath and Wellner Jon A.
Additional contact information
Banerjee Moulinath: University of Michigan
Wellner Jon A.: University of Washington

The International Journal of Biostatistics, 2005, vol. 1, issue 1, 29

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.

Keywords: asymptotic distribution; Brownian motion; contiguous alternatives; greatest convex minorant; likelihood ratio statistic; log-likelihood ratio; score statistic; Wald statistic (search for similar items in EconPapers)
Date: 2005
References: View complete reference list from CitEc
Citations: View citations in EconPapers (2)

Downloads: (external link)
https://doi.org/10.2202/1557-4679.1001 (text/html)
For access to full text, subscription to the journal or payment for the individual article is required.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:bpj:ijbist:v:1:y:2005:i:1:n:3

Ordering information: This journal article can be ordered from
https://www.degruyte ... journal/key/ijb/html

DOI: 10.2202/1557-4679.1001

Access Statistics for this article

The International Journal of Biostatistics is currently edited by Antoine Chambaz, Alan E. Hubbard and Mark J. van der Laan

More articles in The International Journal of Biostatistics from De Gruyter
Bibliographic data for series maintained by Peter Golla ().