Before revision:  It captures the tension between the limiting Shannon entropy (H) of the sketch and its normalized Fisher information (I), which characterizes (asymptotically) the variance of a statistically efficient estimator.
After revision:  It captures the tension between the limiting Shannon entropy (H) of the sketch and its normalized Fisher information (I), which characterizes (asymptotically) the variance of a statistically efficient , asymptotically unbiased estimator. Our results are as follows.