Fredholm integral relation between compound estimation and prediction (FIRCEP)

We discuss the following problem: Given a set of information criteria for optimal designs, the numerical and computational complexity may drastically differ from one criterion to another. A general novel methodology, called the "FIRCEP" is introduced, and shown to work satisfactorily on a variety of problems relating weighted estimation criterion and Integrated mean square prediction error (IMSPE) prediction criteria in framework of stochastic process. The FIRCEP is shown to be identifying such relationship and providing the exact relations between estimation and prediction for regression problems with correlated errors, without necessity to have known eigenexpansion and truncation methodology. The latter one is the main drawback for automation of complexity reduction algorithms for IMSPE optimization for kernels with unknown eigenexpansion. Thus FIRCEP fills the gap of missing exact method for general kernel satisfying mild regularity conditions in order to develop relation between a class of integrated compound criteria and IMSPE. The exposition proceeds by a series of numerical and real data examples.