Excessive efficiency in statistical interpolation due to too many constraints

Abstract

A mean function and a variance function are specified which interpolate given points in that the mean function intersects the points and the variance function is zero at the points.  The specification places simple and reasonable constraints on the form of these functions and on the form of their extrapolation.  Using an elementary three-point problem, it is shown that the resulting variance function is unreasonably small over the point domain.  This excessive efficiency illustrates that too many constraints can yield unwarranted and overly-optimistic results in statistical interpolation.