MEASURES OF GLOBAL RELATIVE CURVATURE.
Abstract
The descriptive problem is considered in determining to what extent a convex regression function appears to have smooth change in slope rather than abrupt changes as typified by broken lines. An index of relative curvature is defined which assigns large values to functions having smooth first derivative and which is zero for broken lines. Discrete approximations to this index are considered, depending only on knowledge of the regression function at a finite set of points. Values of these indices are calculated for convex functions obtained from least squares regression fits in models having only the restriction of concavity. A Monte Carlo experiment was conducted to determine the variability of these discrete indices and some numerical results are presented. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Oct 20, 1967
- Accession Number
- AD0660682
Entities
People
- Paul I. Feder
Organizations
- Stanford University