Maximum observed likelihood prediction of future record values

Test, vol. 29, pp. 1072–1097

Abstract

Abstract Point prediction of future upper record values is considered. For an underlying absolutely continuous distribution with strictly increasing cumulative distribution function, the general form of the predictor obtained by maximizing the observed predictive likelihood function is established. The results are illustrated for the exponential, extreme-value and power-function distributions, and the performance of the obtained predictors is compared to that of maximum likelihood predictors on the basis of the mean squared error and the Pitman’s measure of closeness criteria. For exponential and extreme-value distributions, it is shown that under slight restrictions, the maximum observed likelihood predictor outperforms the maximum likelihood predictor in terms of both performance criteria.

Authors 2

1. Grigoriy Volovskiy corresponding Aachen Institute of Statistics

   RWTH Aachen University

   Affiliation as printed

   Institute of Statistics, RWTH Aachen University, 52056, Aachen, Germany

2. Udo Kamps Aachen Institute of Statistics

   RWTH Aachen University

   Affiliation as printed

   Institute of Statistics, RWTH Aachen University, 52056, Aachen, Germany