Non‐parametric confidence estimates for the Gini–Simpson measure of sparsity

Assessment of the quality of local estimates of data sparsity is central for various adaptive algorithms in signal processing. Empirical bounds for the estimation performance of a frequently used measure of sparsity, namely the Gini–Simpson index are derived. Confidence bounds are derived for an unbiased estimator of this measure, with exponential convergence to the true (unknown) sparsity value, as the number of samples increases. The analysis is distribution‐free, as no parametric or distributional assumptions are made for the available data.