Abstract 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.

中文翻译：

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复合估计和预测之间的 Fredholm 积分关系 (FIRCEP)

摘要 我们讨论以下问题：给定一组用于优化设计的信息标准，数值和计算复杂性可能因一个标准而异。引入了一种称为“FIRCEP”的通用新方法，并显示在随机过程框架下与加权估计标准和综合均方预测误差（IMSPE）预测标准相关的各种问题上都能令人满意地工作。FIRCEP 被证明可以识别这种关系，并为具有相关误差的回归问题提供估计和预测之间的确切关系，而无需知道本征展开和截断方法。后一个是复杂度降低算法自动化的主要缺点，用于具有未知特征扩展的内核的 IMSPE 优化。因此，FIRCEP 填补了满足温和正则性条件的通用核缺少精确方法的空白，以发展一类综合复合准则与 IMSPE 之间的关系。阐述通过一系列数值和真实数据示例进行。