We propose a new type of stochastic ordering which imposes a monotone tendency in differences between one multinomial probability and a known standard one. An estimation procedure is proposed for the constrained maximum likelihood estimate, and then the asymptotic null distribution is derived for the likelihood ratio test statistic for testing equality of two multinomial distributions against the new stochastic ordering. An alternative test is also discussed based on Neyman modified minimum chi-square estimator. These tests are illustrated with a set of heart disease data.

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Keywords Kuhn-Tucker conditions, Likelihood ratio test, Neyman modified chi-square estimate, Stochastic ordering
Persistent URL dx.doi.org/10.1007/s00362-011-0380-7
Journal Statistical Papers
Citation
Lee, C.-I.C. (Chu-In Charles), Liu, W. (Wei), Park, C, & Peng, J. (Jianan). (2012). Inference for comparing a multinomial distribution with a known standard. Statistical Papers, 53(3), 775–788. doi:10.1007/s00362-011-0380-7