This paper presents the SCUBEEx rms emittance analysis, a self-consistent, unbiased elliptical exclusion method, which combines traditional data-reduction methods with statistical methods to obtain accurate estimates for the rms emittance. Rather than considering individual data, the method tracks the average current density outside a well-selected, variable boundary to separate the measured beam halo from the background. The average outside current density is assumed to be part of a uniform background and not part of the particle beam. Therefore the average outside current is subtracted from the data before evaluating the rms emittance within the boundary. As the boundary area is increased, the average outside current and the inside rms emittance form plateaus when all data containing part of the particle beam are inside the boundary. These plateaus mark the smallest acceptable exclusion boundary and provide unbiased estimates for the average background and the rms emittance. Small, trendless variations within the plateaus allow for determining the uncertainties of the estimates caused by variations of the measured background outside the smallest acceptable exclusion boundary. The robustness of the method is established with complementary variations of the exclusion boundary. This paper presents a detailed comparison between traditional data reduction methods and SCUBEEx by analyzing two complementary sets of emittance data obtained with a Lawrence Berkeley National Laboratory and an ISIS H{sup -} ion source
