Graduate Thesis Or Dissertation
 

A maximum likelihood approach to prediction with applications to binomial and Poisson populations

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https://ir.library.oregonstate.edu/concern/graduate_thesis_or_dissertations/6q182p035

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  • Given a sample from a population whose distribution belongs to a parametric family we would like to make predictions on the outcome of a statistic (generally the sample sum) of a future sample from the same population. These predictions can be in the form of intervals with some associated level of confidence or in the form of predictive distributions. A "Maximum Likelihood Predictive Distribution" is introduced which is easily accessible in most regular cases and under conditions similar to those for the consistency of the maximum likelihood estimator converges almost surely to the true distribution of the predicted variable when the observed sample size becomes large. The new approach is compared to frequentist and Bayesian approaches and to another likelihood approach introduced by R. A. Fisher. The comparisons are conducted for simple random sampling from Poisson populations and from binomial populations. The various approaches yield quite similar results for all sample sizes and tend to be equivalent to the method using normal approximations when both the observed and future sample sizes tend to infinity such that their ratio remains constant. It is shown that the Maximum Likelihood Predictive Distribution is almost identical to the Bayesian predictive distribution under prior √λ in the Poisson case and prior √p(1 - p) in the binomial case. These approaches are also considered for Poisson and binomial stratified random sampling and the results compared.
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