Predictive inferences for future outcomes utilizing the past data and simulation
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Date
2011
Authors
Nechval, K.N.
Nechval, N.A.
Purgailis, M.
Strelchonok, V.F.
Berzins, G.
Moldovan, M.
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Conference paper
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Proceedings of the 11th International Conference Reliability and Statistics in Transportation and Communication, 2011, pp.45-59
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11th International Conference "Reliability and Statistics in Transportation and Communication" (RelStat'11) (19 Oct 2011 - 22 Oct 2011 : Riga, Latvia)
Abstract
In this paper, we consider the problems of constructing predictive inferences for future outcomes from invariant distributions via the conditional as well as unconditional approaches. It is assumed that only the functional form of the 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. The technique proposed here for constructing predictive inferences for future outcomes via the conditional approach emphasizes pivotal quantities relevant for obtaining ancillary statistics and represent a special case of the method of invariant embedding of sample statistics into a performance index applicable whenever the statistical problem is invariant under a group of transformations, which acts transitively on the parameter space. It requires the use of numerical integration, but computing time is small. The method is applicable very generally to censored as well as uncensored data, is exact (i.e. requires no asymptotic approximations), and uses all the information in the past data.
The technique proposed here for constructing predictive inferences for future outcomes via the unconditional approach represents a simple procedure that can be utilized by non-statisticians, and which provides easily computable explicit expressions for both prediction bounds and prediction intervals via simulation and the past data. Although computation of the maximum likelihood estimates and determination of needed percentiles via simulation require a computer, we assert that the proliferation of personal computers makes these procedures more convenient than alternative procedures in the literature which require several specialized tables. This is particularly true for censored samples, since then the needed tables are generally incomplete and interpolation is required. Simulation may be used in all situations, i.e., any sample, any level of Type II censoring, and any order statistic from a future sample. Results of an empirical study show that in many practical situations the two approaches considered lead to near-equivalent results. An illustrative example is given.
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Copyright 2011 Transport and Telecommunication Institute