Hirschman–Herfindahl index determination under incomplete information

Abstract

This paper utilizes techniques from combinatorics to derive a closed form solution for an estimator of that portion of a Hirschman–Herfindahl index which measures concentration for that segment of the market with unattributed market share. This index makes more complete use of sample information than other more conventional measures of limited-information market concentration like the C₄ and C₈ indices.