Optimal third root asymptotic bounds in the statistical estimation of thresholds
阈值统计估计的最优立方根渐近界
This paper is concerned with estimating the intersection point of two densities, given a sample of both of the densities. This problem arises in classification theory. The main results provide lower bounds for the probability of the estimation errors to be large on a scale determined by the inverse cube root of the sample size. As corollaries, we obtain probabilistic bounds for the prediction error in a classification problem. The key to the proof is an entropy estimate. The…