Confidence Sets for Statistical Classification
Round 1
Reviewer 1 Report
The addition of simulation results has improved the paper a lot.
Author Response
Thank you very much
Reviewer 2 Report
Still the answer about parameters S and Q appears to be very experimental in nature.
Author Response
At the end of the 2nd paragraph on Page 17 of this revision, we have added
{\bf It must be pointed out that there is no easy way to assess how theaccuracy of $\lambda$ depends on the values of $S$ and $Q$.One practical way is to compute several $\lambda$-values usingdifferent random seeds in the simulation for given $S$ and $Q$.These $\lambda$-values provide information on the variability andso accuracy of $\lambda$ due to simulation randomness. See moredetails in Section 5} to pint out the fact there is no simple way toassess how the accuracy of $\lambda$ depends on the values of $S$ and $Q$.
Reviewer 3 Report
This manuscript discusses the classification problem and proposes a new classifier that classifies an observation into one or more categories based on a confidence set of the true class of the observation. The confidence set is constructed by inverting a family of acceptance sets. The proposed approach is innovative and interesting, especially useful when there is a similar chance of an observation belonging to two or more classes. I only have a minor comment: the use of ‘p’ is a bit confusing. On Page 22, ‘p’ is defined as ‘the proportion of correct classification’ while earlier ‘p’ is defined to be the dimension of the vector x_i. It would be clearer to use a different notation.
Author Response
In this revision, this $p$ has been replaced by $\zeta$.
