Optimal Estimators of Cross-Partial Derivatives and Surrogates of Functions

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

This paper  introduces surrogates of cross-partial derivatives for every smooth function by evaluating that  function at randomized points, which are based on independent, central-symmetric variables and a set of constraints. This paper has the new results and good presentation. I suggest accept in current form.

Author Response

(x) I would not like to sign my review report
( ) I would like to sign my review report

Quality of English Language

( ) I am not qualified to assess the quality of English in this paper
( ) English very difficult to understand/incomprehensible
( ) Extensive editing of English language required
( ) Moderate editing of English language required
( ) Minor editing of English language required
(x) English language fine. No issues detected

	Yes	Can be improved	Must be improved	Not applicable
Does the introduction provide sufficient background and include all relevant references?	(x)	( )	( )	( )
Is the research design appropriate?	(x)	( )	( )	( )
Are the methods adequately described?	(x)	( )	( )	( )
Are the results clearly presented?	(x)	( )	( )	( )
Are the conclusions supported by the results?	(x)	( )	( )	( )

Comments and Suggestions for Authors

This paper  introduces surrogates of cross-partial derivatives for every smooth function by evaluating that  function at randomized points, which are based on independent, central-symmetric variables and a set of constraints. This paper has the new results and good presentation. I suggest accept in current form.

Thanks !

Reviewer 2 Report

Comments and Suggestions for Authors

Manuscript title: Optimal Estimators of Cross-Partial Derivatives and Surrogates of Function (stats-3060571)

Journal: Stats

 

1) The abstract requires improvement. Please rephrase it, emphasizing the manuscript's significance and highlighting the attained results.

2) Kindly restructure the introduction section and incorporate contemporary references that fulfill the intended purpose.

3) Self-citations should be minimized as much as possibleز

4) On what basis were the randomized points chosen to evaluate the every smooth function after computing  the cross-partial derivatives for it?

5) What is the importance of the proposed new expressions of cross-partial derivatives of any order? Are there conditions for application? Please give more details.

6) Are there other studies that have dealt with this expressions of cross-partial derivatives of any order? If there are other studies, they should be mentioned.

7) The statistical package/software used for the simulation study should be mentioned.

Author Response

Open Review

(x) I would not like to sign my review report
( ) I would like to sign my review report

Quality of English Language

(x) I am not qualified to assess the quality of English in this paper
( ) English very difficult to understand/incomprehensible
( ) Extensive editing of English language required
( ) Moderate editing of English language required
( ) Minor editing of English language required
( ) English language fine. No issues detected

	Yes	Can be improved	Must be improved	Not applicable
Does the introduction provide sufficient background and include all relevant references?	( )	( )	(x)	( )
Is the research design appropriate?	( )	( )	(x)	( )
Are the methods adequately described?	( )	( )	(x)	( )
Are the results clearly presented?	( )	(x)	( )	( )
Are the conclusions supported by the results?	( )	(x)	( )	( )

Comments and Suggestions for Authors

Manuscript title: Optimal Estimators of Cross-Partial Derivatives and Surrogates of Function (stats-3060571)

Journal: Stats

 

1) The abstract requires improvement. Please rephrase it, emphasizing the manuscript's significance and highlighting the attained results.

 

Done, and thanks !

 

2) Kindly restructure the introduction section and incorporate contemporary references that fulfill the intended purpose.

 

Done, and thanks !

 

3) Self-citations should be minimized as much as possibleز

I agrée, but such references are relevant for such a topic.

 

4) On what basis were the randomized points chosen to evaluate the every smooth function after computing  the cross-partial derivatives for it?

Sorry, I did not understand this question.

 

5) What is the importance of the proposed new expressions of cross-partial derivatives of any order? Are there conditions for application? Please give more details.

Yes, for functions with full interactions (see introduction).

 

6) Are there other studies that have dealt with this expressions of cross-partial derivatives of any order? If there are other studies, they should be mentioned.

Yes, see page 2 of introduction.

7) The statistical package/software used for the simulation study should be mentioned.

See  reference 59.

Reviewer 3 Report

Comments and Suggestions for Authors

The content of this paper is outside my area of expertise, so, I can't judge the relevance of the paper. However, as far as I can see the proofs are correct except for some minor typos - e.g., it should be p >= 0 in line 363? Also the text may need some minor edits - e.g., what does 'ANOVA and sensitivity analysis communities' mean? May be 'ANOVA and sensitivity analyses user communities'?

Comments on the Quality of English Language

Minor edits required

Author Response

x) I would not like to sign my review report
( ) I would like to sign my review report

Quality of English Language

( ) I am not qualified to assess the quality of English in this paper
( ) English very difficult to understand/incomprehensible
( ) Extensive editing of English language required
( ) Moderate editing of English language required
(x) Minor editing of English language required
( ) English language fine. No issues detected

	Yes	Can be improved	Must be improved	Not applicable
Does the introduction provide sufficient background and include all relevant references?	(x)	( )	( )	( )
Is the research design appropriate?	(x)	( )	( )	( )
Are the methods adequately described?	(x)	( )	( )	( )
Are the results clearly presented?	( )	( )	( )	( )
Are the conclusions supported by the results?	(x)	( )	( )	( )

Comments and Suggestions for Authors

The content of this paper is outside my area of expertise, so, I can't judge the relevance of the paper. However, as far as I can see the proofs are correct except for some minor typos - e.g., it should be p >= 0 in line 363? Also the text may need some minor edits - e.g., what does 'ANOVA and sensitivity analysis communities' mean? May be 'ANOVA and sensitivity analyses user communities'?

Thanks for the proofs!

Sentences have been improved.

 

Round 2

Reviewer 2 Report

Comments and Suggestions for Authors

No additional comments.