Asymptotic Treatment for Multinomial Models and Applications - Akoto, Isaac (2022)
In this study, we derived a highly convenient chi-square test to replace the Ftests for an Analysis of Variance (ANOVA)-like inference for multinomial models. To obtain these results we started by studying limit distributions in models with compact parameter space. Based on these results we obtained confidence ellipsoids and simultaneous confidence intervals for models with limit normal distributions. Next, we studied the covariance matrices of the limit normal distributions for the multinomial models. This was a transition between the previous general results and those on the inference for multinomial models in which we considered the chi-square tests, confidence regions and non-linear statistics, namely log-linear model, with two numerical applications to those models. Our approach overcame the hierarchical restrictions assumed to analyze multidimensional contingency table. Also, by application for our research, we developed Discriminant Analysis (DA) for samples extracted from a random variable which can only take a finite number of values so a sample constituted by such values will have a multinomial distribution M( jn;p), with n being the sample size and p the probabilities of having the different values. Using DA in connection with Statistical Decision Theory (SDT), since we aim at minimizing the average cost associated with decisions, we derived a rule that minimizes the assignment costs. Our results were applied to data on Human Immunodeficiency Virus (HIV) treatments, and classified patients into Treated or Naive populations at an accuracy of 71.06%, despite the peculiar nature of our dataset. We also were able to show that our discrimination procedure was consistent.