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On efficient point prediction systems
Author(s) -
Skouras K.,
Dawid A. P.
Publication year - 1998
Publication title -
journal of the royal statistical society: series b (statistical methodology)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 6.523
H-Index - 137
eISSN - 1467-9868
pISSN - 1369-7412
DOI - 10.1111/1467-9868.00153
Subject(s) - sequence (biology) , point (geometry) , parametric statistics , independence (probability theory) , computer science , class (philosophy) , bayesian probability , mathematics , random variable , prediction interval , mathematical optimization , statistics , artificial intelligence , machine learning , genetics , geometry , biology
Assume that a forecaster observes a sequence of random variables and issues predictions according to a point prediction systems, i.e. a rule which, at every time t , issues a point prediction for the next observation at time t +1. We introduce the concept of efficiency of a point prediction system, for the case that the joint distribution of the sequence of observations is known to belong to a parametric family, and performance is assessed by the long run sum of squared prediction errors. Independence is not a requirement. Under weak conditions, the class of efficient point prediction systems is non‐empty, and any two efficient point prediction systems will, in a certain strong sense, make asymptotically identical predictions for the infinite future. We discuss the efficiency of point prediction systems based on Bayesian predictive means, and on plugging in parameter estimates. The results are applied to probability forecasting and stochastic regression.