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July, 1978 Testing a Linear Constraint for Multinomial Cell Frequencies and Disease Screening
Jerome H. Klotz
Ann. Statist. 6(4): 904-909 (July, 1978). DOI: 10.1214/aos/1176344263


For comparing two disease screening procedures with economic costs assigned to administration, false positives, and false negatives, the problem of testing a linear cell frequency constraint $\sum^K_{i = 1} a_i p_i \leqq 0$ arises with the multinomial $(n, (p_1, p_2,\cdots, p_K))$ model. An ad hoc statistic based upon the estimate of the $p_i$ values, $\sum^K_{i = 1} a_i X_i/n,$ is compared with the likelihood ratio statistic $-2\ln \lambda,$ the latter having an interesting form. For local (contiguous) alternatives the two statistics have similar large sample properties. However, the likelihood ratio statistic has greater large deviation efficiency for fixed alternatives and is recommended.


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Jerome H. Klotz. "Testing a Linear Constraint for Multinomial Cell Frequencies and Disease Screening." Ann. Statist. 6 (4) 904 - 909, July, 1978.


Published: July, 1978
First available in Project Euclid: 12 April 2007

zbMATH: 0378.62023
MathSciNet: MR494636
Digital Object Identifier: 10.1214/aos/1176344263

Primary: 62F05
Secondary: 62P10

Keywords: disease screening , efficiency , Information , large deviations , likelihood ratio test , linear constraint , Multinomial , testing

Rights: Copyright © 1978 Institute of Mathematical Statistics


Vol.6 • No. 4 • July, 1978
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