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

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.