Graduate Thesis Or Dissertation
 

Prediction intervals in exponential families

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  • Prediction intervals for an outcome of a sufficient statistic, T[subscript y], associated with the probability distribution of a future experiment are developed based on information obtained from n independent, previously conducted trials of an informative experiment. The random outcomes of the informative and future experiments are assumed to be continuous and identically distributed according to a ICparameter exponential family, and the future experiment is conducted independent of the informative experiment. These intervals are of the general forms, S₁(t[subscript x])=[L.(t[subscript x]),∞), S₂(t[subscript x])=(-∞,IU(t[subscript x])] and S₃(t[subscript x])=[L(t[subscript x]),U(t[subscript x])] where U(.), L(.) are functions of t[subscript x] , the observed value of a sufficient statistic for the joint probability distribution of the random outcomes from the informative experiment. A general theory and procedure for deriving these prediction intervals is developed using hypothesis testing procedures. Optimal properties of hypothesis tests carry over to similarly defined optimal properties of prediction intervals. The intervals have the 'similar mean coverage' property (Aitchison, J. and Dunsmore, I.R. (1975)). The generalized Newton's method and the IMSL routines are used for numerical computation of tables for the examples considered. An application of the saddle point approximation, Barndorff Nielsen, 0. (1983), for finding an approximate conditional density function for sufficient statistics associated with the probability distribution of the experiments is discussed.
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