Depth Induced Regression Medians and Uniqueness
Round 1
Reviewer 1 Report
The paper is well written and organized, I found only "technical" problems 1) I did not find abstract, title and keywords, 2) I could not see Figures 2 and 3.
Minor comments:
line 13: It might be usefull to recall how the quantile is defined. What if we consider a uniform distribution on (0,1)U(2,3). What is the value of median in this case?
line 16: brackets: (Donoho (1982)) - delete two additional )(
line 21: and -> an
line 64-65: monotonicity relative to the deepest point,
line 85: bracket ) in lower index is missing
line 106: for thought: What can be said about theoretical (not sample) medians?
line 122: How instead of What ?
line 156: comma missing in (-7.4, 2.8)
line 170: previous instead of last ?
line 170: multiple
line 211: a bit clumsy expression "bounded beta_0"
line 213-214: What is G? There should be PRD on both sides.
line 214: PRD(beta*,...) ?
line 214: Why the symbol of square?
lines 218, 220, 221: Lemma 4.1, not 3.1
line 219: contradiction
line 232: (A2)
Author Response
Please see the attached file for my point-by-point response to your report.
For your convenience, the revised manuscript has also merged with the response
file.
Author Response File: 
Author Response.pdf
Reviewer 2 Report
"Regression medians and uniqueness" by Zuo (2020)
The author presented some interesting uniqueness properties of Depth Regression medians modelling. Depth feature serves as a good alternative for classical least squares estimator. The author presented in clear and well form the propositions. However, the examples lack of statistical analysis: fit, estimation, residuals inspection, etc.
I recommends to author to improve this aspect to complete the manuscript, and submit to STATS again. Then I could review a new version of this manuscript.
Some minor comments:
- Improve the title, please do it more representative. For example: "Depth induced Regression medians and uniqueness".
- P1 L8: DC not defined.
- Eq (1): write the regression with the observations i=1,...,n.
- P2 L38: Use \top for transposed vector/matrix.
- Fix the reference's citations in the body's manuscript.
Author Response
Please see the attached my point-by-point responses to your report.
For your convenience, the revised manuscript has also provided at the end of the response file.
Author Response File: Author Response.pdf
Round 2
Reviewer 2 Report
2nd review of: "Depth induced regression medians and uniqueness" by Zuo (2020)
In this new review, I see that author addressed several aspects related to my last review. However, I don't convinced with their reply to my first question. He said: "... these tedious details do not deserve to be published and thus are
omitted..."
I don't believe that these "details" are tedious or can be ommited. In any new modelling, it is important to shows the model's development on a real-life dataset. For this reason, I cannot recommends the publication of this manuscript is STATS.
Author Response
please see the attached file of my response to the reviewer
Author Response File: Author Response.pdf
Round 3
Reviewer 2 Report
Dear author,
thanks for provides final details about regression. Now, I could recommend the publication of this manuscript. I have only 1 minor comment:
- Figure 3, in title: fix "medains" by "medians". Also, put ix X and Y axis: log(Te) and log(Light).
