Inference for comparing a multinomial distribution with a known standard

• Published in: Statistical papers (Berlin, Germany) Vol. 53; no. 3; pp. 775 - 788
• Main Authors: Lee, Chu-In Charles, Liu, Wei, Park, Chul Gyu, Peng, Jianan
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer-Verlag 01-08-2012; Springer Nature B.V
• Subjects: Asymptotic methods; Cardiovascular disease; Economic Theory/Quantitative Economics/Mathematical Methods; Economics; Finance; Insurance; Management; Mathematics; Mathematics and Statistics; Operations Research/Decision Theory; Probability; Probability Theory and Stochastic Processes; Regular Paper; Statistics; Statistics for Business; Stochastic models; Studies; 60E15; Stochastic ordering; Kuhn-Tucker conditions; 62G10; Neyman modified chi-square estimate; Likelihood ratio test
• ISSN: 0932-5026; 1613-9798
• DOI: 10.1007/s00362-011-0380-7

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.