Efficient Predictive Inferences for Future Outcomes Under Parametric Uncertainty of Underlying Models

Abstract

Predictive inferences (predictive distributions, prediction and tolerance limits) for future outcomes on the basis of the past and present knowledge represent a fundamental problem of statistics, arising in many contexts and producing varied solutions. In this paper, new-sample prediction based on a previous sample (i.e., when for predicting the future outcomes in a new sample there are available the observed data only from a previous sample), within-sample prediction based on the early data from a current experiment (i.e., when for predicting the future outcomes in a sample there are available the early data only from that sample), and new-within-sample prediction based on both the early data from that sample and the data from a previous sample (i.e., when for predicting the future outcomes in a new sample there are available both the early data from that sample and the data from a previous sample) are considered. It is assumed that only the functional form of the underlying distributions is specified, but some or all of its parameters are unspecified. In such cases ancillary statistics and pivotal quantities, whose distribution does not depend on the unknown parameters, are used. In order to construct predictive inferences for future outcomes, the invariant embedding technique representing the exact pivotal-based method is proposed. In particular, this technique can be used for optimization of inventory management problems. A practical example is given.