Scalar-on-Function Relative Error Regression for Weak Dependent Case
, Fatimah Alshahrani 2, Ibrahim M. Almanjahie 1, Zoulikha Kaid 1, Ali Laksaci 1 and Mustapha Rachdi 3,*Round 1
Reviewer 1 Report
After some minor revisions, the paper can be accepted. Below are my suggestion for revisions.
Line 48 The authors wrote “This paper is structured as follows.” It is better to write “This paper is organized as follows”.
Line 53 I think the title “The model and its kernel smoothing in quasi-associated functional time series” can be improved.
Line82 “based on” should be “Based on”.
Line85 , Line92 “Lemmas” should be “lemmas”
Lemma 4. “based on” should be “Based on”.
Page11 “in this appendix,” should be “In this appendix,”.
I think the presentation of the abstract can be improved.
Author Response
Please, see the joined file containing the point-by-point responses to the referees requests.
Author Response File: 
Author Response.pdf
Reviewer 2 Report
Title: Scalar-on-function relative error regression for weak dependent case
By: Zouaoui Chikr Elmezouar, Fatimah Alshahrani, Ibrahim M. Almanjahi,
Zoulikha Kaid, Ali Laksaci and Mustapha Rachdi
Submitted to: Axioms
MS I.d. axioms-2374615
Report: 05/15/2023
To study the co-variability between the Hilbert regressor and the scalar output
variable, the authors propose the kernel smoothing of the Relative Error Regression
(RE-regression) method. Selecting the smoothing parameter is discussed, and a
simulation investigation is performed to examine the behavior of the RE-regression
estimation and its superiority in practice.
Major Comments:
* As the RE-regression is a well studied topic, the authors only made extension of
it to the case of weak dependent. The novelty is limited.
* The authors should discuss the advantage(s) and dis-advantage(s) of using
RE-regression vs the traditional regression.
* How to check condition (D3)? Also conditions (D5)-(D7) are strong and not easy
to check.
* In Theorem 1, the convergence rate is slow, as typically h_n=O(n^{1/5}); the
2nd term is also slower than the typical rate of kernel estimator.
* Can the authors derive asymptotic distribution of \hat{R}_D(x)?
Minor Comments:
* The presentation needs improvement. For example, condition (D1), "such that" is
not needed. Also, is this condition uniformly over x? Condition (D2), "we have"
is not needed.
* Section 5.1, expression (1). Please mention that \tau(.) is a given function.
Please describe what is \epsilon_i?
* The presentation needs improvement. For example, condition (D1), "such that" is
not needed. Also, is this condition uniformly over x? Condition (D2), "we have"
is not needed.
* Section 5.1, expression (1). Please mention that \tau(.) is a given function.
Please describe what is \epsilon_i?
Author Response
Please, see the joined file containing the point-by-point responses to the referees requests.
Author Response File: Author Response.pdf
Reviewer 3 Report
Please, read the attached file review.pdf.
Comments for author File: Comments.pdf
The English language needs little editing. I explain this in my report.
Author Response
Please, see the joined file containing the point-by-point responses to the referees requests.
Author Response File: Author Response.pdf
Reviewer 4 Report
In this work authors have provided a new predictor in the Hilbertian time series, which is an alternative to classical regression based on conditional expectation. They have clearly justified their claim that this new estimator increased the robustness of the classical regression because it reduced the effect of the largest variables. Both the Theorems 1 and 2 and supporting Lemmas 1-4 are good results, proofs of the Lemmas are not elementary. As far as I could check there are no mistakes in the paper. However, it will help the readers if authors properly define the constants $k_1$ and $k_2,$ also some upper bounds for $\xi_1$ and $xi_2.$
Author Response
Please, see the joined file containing the point-by-point responses to the referees requests.
Author Response File: Author Response.pdf
