Optimal allocation of fresh interviews across injection times

Determine how to distribute a fixed budget of fresh interviews across injection times to maximize information about the drift coefficient in the additive panel design.

Background

The paper studies how refreshment schedules affect identification of the conditioning path in an additive cell-mean model. Although the rank of a proposed schedule can determine which functionals of the conditioning path are identified, the paper does not solve the related experimental-design problem of choosing injection times when the number of fresh interviews is fixed.

The authors report numerical evidence suggesting that two injections at maximal temporal spread may be optimal, but they explicitly state that this has not been proved. The unresolved problem is therefore to derive and establish an optimal allocation rule, rather than merely to characterize identification for a given schedule.