Statistical comparison of counting and record-time estimators

Determine whether the statistical estimators based on integrated-current counting and inter-record-time measurements exhibit different convergence properties or provide a statistical advantage over one another.

Background

The paper establishes an exact equivalence between the asymptotic precision of an integrated current and the squared coefficient of variation of its inter-record times in finite-state continuous-time Markov jump processes. Although the two descriptions are mathematically equivalent at the level of precision, they rely on different empirical data: current-based estimation uses long-time counting statistics, whereas record-time estimation uses independent inter-record intervals that can be measured over finite observation periods.

The authors explicitly leave unresolved whether one of these approaches offers a practical statistical benefit. The open problem concerns a systematic comparison of the convergence properties of the corresponding estimators and whether either measurement strategy yields superior statistical performance. This question is not addressed by the exact equivalence proved in the paper.