Algebraic Derivation of Elfving Theorem on Optimal Experiment Design and Some Connections With Sparse Estimation

Elfving theorem is a fundamental result in the area of optimal experiment design, and yet its available proofs require a number of somewhat indirect geometrical arguments that might detract a potential user from its full understanding and exploitation. In this letter, we provide a direct algebraic proof of this theorem. Furthermore, we make some connections with the ℓ₁- norm minimization approach commonly used for sparse estimation, which suggest importation of algorithms and results from the latter area into that of optimal experiment design.