| Summary: | 碩士 === 國立交通大學 === 統計學研究所 === 93 === Generalizing from Chen (2004) of dealing for continuous distributions, we introduce a likelihood-based confidence set for the discrete distributions. Besides some properties extended from maximum likelihood estimator, four additional properties are of special interest. First, this set is shown to have volume for the sample falling in the confidence set the smallest among classes of 100(1-α)% confidence sets. With the fact that expected-length is a popularly used criteria for comparing confidence intervals and, actually, there is no satisfactory results for constructing the optimal one, minimizing the volume, in terms of sample x, is a good criterion for evaluating confidence interval for discrete distributions. Second, the likelihood-based confidence sets include maximum likelihood estimate, the most plausible parameter value after an observation has been made, whereas the traditional frequentist approaches of confidence set are criticized for that may not include it. Third, the construction of these confidence sets are based on Fisher's likelihood principle which ask that any statistical procedure should depend upon the likelihood function whereas the existed confidence sets do not fulfill this desirability. Fourth, properties behaving for maximum likelihood estimator such as invariance and sufficiency have been carried over to these approaches. The property of invariance is interesting for the fact that the Bayesian highest posterior density confidence set has also an optimality of shortest width, however, this Bayesian interval is criticized for depending on the prior density and for not having the desired property of invariance.
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