Nonparametric Estimation IV

In the three papers, 1, 2, 3, entitled "Nonparametric estimation", Scheffe and Tukey generalized previous results on tolerance regions and extended them to cover all continuous and discontinuous distribution functions. This note contains four comments arising from these papers: first, on a method for giving bounds to the confidence level in the discontinuous case which can lower the probability that the end points need to have part, a random variable, of their probability neglected to maintain the given confidence level; second, on a correction of a statement of results in 2; third, on a proof in 2 requiring a further statement; fourth, a necessary restatement of theorems in 3.