The Nu Class of Low-Degree-Truncated, Rational, Generalized Functions. I. IMSPE in Design of Computer Experiments: Integrals and Very-Low-N, Single-Factor, Free-Ranging Designs

2016/04/18 by Selden Crary, Crary, Selden
Mathematics · #FOS: Computer and information sciences #Methodology (stat.ME) #stat.ME

paper · pdf · doi:10.48550/arxiv.1604.05278

61 pages, 5 figures, 20 appendices

arxiv created 2019/05/16 · arxiv updated 2019/05/20

Abstract

We provide detailed algebra for determining the integrated mean-squared prediction error (IMSPE) of designs of computer experiments, with one factor and one or two points, under the exponential, Gaussian, or either of two Matern correlation functions. This algebra shall provide the basis for the identification of the IMSPE as a member of a special class of low-degree-truncated rational functions, which we name, here, the Nu class. We shall detail this function class in a series of papers, of which this is the first.

Related

• The Nu Class of Low-Degree-Truncated, Rational, Generalized Functions. Ib. Integrals of Matern-correlation functions for all odd-half-integer class parameters
• Fonctions spéciales et polynômes orthogonaux: cours et exercices corrigés
• Applications of certain probability distributions on positive integers
• Orthogonal polynomials, special functions and mathematical physics
• Scaling up to Multivariate Rational Function Reconstruction