Optimal configurations of lines and a statistical application

TL;DR

This paper investigates optimal arrangements of lines in real projective space to improve the construction of confidence intervals, providing numerical solutions and verifying their effectiveness in statistical bounds.

Contribution

It introduces a method to find optimal line configurations in real projective space for small dimensions, aiding statistical confidence interval construction.

Findings

Numerical optimal configurations for small dimensions are identified.

The configurations help assess the tightness of statistical bounds.

Results improve understanding of line arrangements in projective space.

Abstract

Motivated by the construction of confidence intervals in statistics, we study optimal configurations of $2^d-1$ lines in real projective space $RP^{d-1}$. For small $d$, we determine line sets that numerically minimize a wide variety of potential functions among all configurations of $2^d-1$ lines through the origin. Numerical experiments verify that our findings enable to assess efficiently the tightness of a bound arising from the statistical literature.