Protection against disclosure is a legal and ethical obligation for agencies releasing microdata files for public use. Any decision about releasing data  is supported by the estimation of measures of disclosure risk. The most common measure is arguably the number $\tau_{1}$ of sample unique records that are population uniques. We first study nonparametric estimation of $\tau_{1}$. We introduce a class of linear estimators of $\tau_{1}$ that are simple, computationally efficient and scalable to massive datasets, and we give uniform theoretical guarantees for them. We then establish a lower bound for the minimax NMSE for the estimation of $\tau_{1}$.