A New Quantile-Based Approach for LASSO Estimation
, Hina Naz 1,†, Sajid Ali 1,*,†, Amani Almohaimeed 2,*,†and Showkat Ahmad Lone 3,†Round 1
Reviewer 1 Report
the article is devoted to the actual topic, but very poorly written.
I have the following remarks
1. Why is underscore used in equation (1) to denote vectors. This designation is not generally accepted.
2. What assumptions does X satisfy? matrix x*x is maritsa full rank?
3. Transposition has two different designations with a stroke and the letter t.
4. Line 118 missing matrix inversion in OLS estimate
5. Eigenvalues have three different designations in
lines 109, 114 and 123.
6. Line 110 W denotes a matrix with eigenvalues.
Equation (12) W already stands for another number!
Explain the essence of your method, why it should work better?
how are percentiles calculated?
Author Response
We thank you for your constructive comments and suggestions that improve our manuscript's quality. In addition, we are highly thankful to you for your careful reading of our paper. Please find atached our response to the revision.Author Response File: 
Author Response.pdf
Reviewer 2 Report
The authors propose an improved method of LASSO to overcome the problem of multicollinearity pair parameter estimation in multiple linear regression task. The manuscript is innovative and well written. However, there are some issues that need to be revised by the authors to improve the quality:
please refer to "peer-review-27619478.v1.docx".
Comments for author File: 
Comments.docx
Author Response
We are highly thankful for your encouraging comments. Your constructive comments and suggestions greatly improved our manuscript's quality. In addition, we are highly grateful to you for your careful reading of our paper. Please find attached our response to the revision.
Author Response File: Author Response.pdf
Round 2
Reviewer 1 Report
The authors have done a lot of work to correct the article, but there are still a number of suggestions.
1. Paragraph 2.1. should be described in more detail is your main result. Give explicit formulas for percentiles. I can’t understand from the article what is P05 or Q2 and what does H have to do with it? Save your reader the trouble of looking it up elsewhere.
2. Why do you think the 5 percentile is the best? Perhaps 3 percent or 10 percent would be better? Or will it be different for different tasks?
Perhaps it is worth bringing the figure of the dependence of the ITU on the percentile?
Author Response
Please find the attached file. Thank you so much for your time and constructive comments.
Author Response File: Author Response.pdf
Round 3
Reviewer 1 Report
Accept in present form
