Parameter Estimation in Spatial Autoregressive Models with Missing Data and Measurement Errors
Round 1
Reviewer 1 Report
Comments and Suggestions for AuthorsPlease see attached.
Comments for author File: 
Comments.pdf
Please see the report.
Author Response
Sincerely thank you for your diligent work and valuable comments!
Responses to your comments have been provided, along with detailed explanations in the attachments.
Please see the attachment.
Author Response File: Author Response.pdf
Reviewer 2 Report
Comments and Suggestions for AuthorsThe authors proposed a parameter estimation method in spatial autoregressive models with missing data and measurement error.
There are several places where notations are not used correctly on page 7.
1. In the equation (2.10), the term on the right-hand side should be L(beta, X, Y), not L(beta, Z, Y).
2. In (2.11), the same mistake was found, the term on the right should be U(beta, X, Y). Also in (2.12), it should be I(beta, X,Y).
3. In (2.13), the term in the middle, it should be U*, not U, the term on the right should be E+{U(beta,X,Y)}.
4. In line 259 in page 7, what do you mean by "differentiable on F"?
5. In line 260, U*(...)=0 converges in probability to 0 -> U*(..) converges in probability to zero.
6. In line 263, "they follow an asymptotic normal distribution with mean" -> does beta* and beta_x converge to 0?
Author Response
Thank you for providing us with valuable feedback, allowing us the opportunity to revise our paper. The responses to your comments are as follows.
comment1.In the equation (2.10), the term on the right-hand side should be L(beta, X, Y), not L(beta, Z, Y).
response1.Thank you for pointing out this mistake. We have corrected it in the manuscript. Please refer to Equation 2.10 on page 7.
comment2.In (2.11), the same mistake was found, the term on the right should be U(beta, X, Y). Also in (2.12), it should be I(beta, X,Y).
response2.Thank you for pointing out this mistake. We have corrected it in the manuscript. Please refer to Equation 2.11 on page 7.
comment3.In (2.13), the term in the middle, it should be U*, not U, the term on the right should be E+{U(beta,X,Y)}.
response3.Thank you very much for your comments. We have corrected it in the manuscript. Please refer to Equation 2.13 on page 7.
comment4.In line 259 in page 7, what do you mean by "differentiable on F"?
response4.We discovered that F was not defined. We have corrected it in the manuscript.Please refer to line 259 on page 7.
comment5.In line 260, U*(...)=0 converges in probability to 0 -> U*(..) converges in probability to zero.
response5.Thank you very much for your comments. We have corrected it in the manuscript.Please refer to line 261 on page 7.
comment6.In line 263, "they follow an asymptotic normal distribution with mean" -> does beta* and beta_x converge to 0?
response6.Thank you for pointing out this mistake. We have corrected it in the manuscript. Please refer to line 265 on page 7.
Reviewer 3 Report
Comments and Suggestions for AuthorsThe problem of parameter estimation of spatial autoregressive models attracts much attention as it is important for the practice. In the practical applications one often has missing data and/or measurement errors. Thus, there is significant amount of research on such problems.
The main point of this manuscript is the used parameter estimation methods, which uses a combination of corrected likelihood estimation and
inverse probability weighting with mean imputation to eliminate biases caused by missing data and measurement errors.
The manuscript is clearly written with large introduction section and emphasis on the development of the research on this problem in China. The main result is given in Section 2. The following two sections are devoted to Monte Carlo simulations which are often used in this kind of studies and to application to real life example - Boston housing data. The results from these two sections show that the methodology works satisfactory well.
Then, my opinion about the publication of the manuscript is positive. I have several technical remarks.
1. The oracle properties are mentioned in the abstract and in the text. Several more explanatory words in the text will be helpful as the theorem in Section 2 mentions such properties
2. Several more explanatory word about GMM and 2SLS will b helpful for the readers who are not specialist in the area of time series analysis.
3. The same about DBSCAN and KNN in the last paragraph of page 3.
4. The DOI of the references are not included. Please format the references according to the requirements of the Journal. Ref. 23 is a dissertation. Is this the full name of this reference?
Author Response
Thank you for providing us with valuable feedback, allowing us the opportunity to revise our paper. We are deeply grateful for the thorough review of the entire manuscript by the reviewers and the beneficial suggestions received. The responses to your comments are as follows.
comment1. The oracle properties are mentioned in the abstract and in the text. Several more explanatory words in the text will be helpful as the theorem in Section 2 mentions such properties.
response1. Thank you for your comments! We have enriched the related content in the article. Please refer to it in the new manuscript.
comment2. Several more explanatory word about GMM and 2SLS will b helpful for the readers who are not specialist in the area of time series analysis.
response2. Thank you for your comments. We have enriched the related content in the article. Please refer to it in the line 56 to 61 on page 2.
comment3. The same about DBSCAN and KNN in the last paragraph of page 3.
response3. Thank you for your comments. We have enriched the related content in the article. Please refer to it in the line 138 to 142 on page 3.
comment4. The DOI of the references are not included. Please format the references according to the requirements of the Journal. Ref. 23 is a dissertation. Is this the full name of this reference?
response4. Thank you for pointing out this mistake. We have corrected it in the manuscript. Please refer to the references section.
Reviewer 4 Report
Comments and Suggestions for AuthorsThe handling of missing data and measurement errors is a serious problem in practical applications. However, the novelty in the paper is missing. Further more it was not examined the broad of the applications. I suggest to rewrite the paper considering the similarity of the Assumptions 1 - 9 before Theorem 1.1 and the Assumptions 2.1.1 - 2.1.10 in section 2.1.
Comments on the Quality of English LanguageNeed some improvement.
Author Response
Thank you very much for your comment; your insight is highly valuable to our article. You are correct in noting that the assumptions of these two sections are fundamentally the same. However, this arrangement was made considering the change in symbols, with the aim of facilitating reader comprehension. While we appreciate the suggestion to rewrite the paper considering the similarity of Assumptions 1 - 9 before Theorem 1.1 and Assumptions 2.1.1 - 2.1.10 in section 2.1, we believe that the current structure serves the purpose of clarity and aids in the understanding of the theoretical framework. This approach allows us to maintain the integrity of the methodological exposition without compromising the accessibility of the paper to our intended audience. We hope this clarification addresses your concern, and we have made efforts to ensure that the significance and application breadth of our work are adequately presented within the scope of our study.
Round 2
Reviewer 1 Report
Comments and Suggestions for AuthorsReport on resubmitted version of
Parameter Estimation in Spatial Autoregressive Models with Missing Data and Measurement Error
Tengjun Li, Zhikang Zhang , and Yunquan Song
The current version is not very different from the previous version. It is therefore difficult to understand why an author is dropped from the paper and another author made first author. Many comments are not addressed seriously enough. The present version is hardly an improvement over the original version. In fact it is actually worse than before. Few examples:
l.13. “The former typically assumes that the explained variable are mutually independent.” is both incorrect from a very elementary statistical point of view and from a grammatical point of view. A single variable cannot be independent. Independent observations are intended presumably, but this is not stated which is bad. From a grammatical point of view it is also incorrect using the singular “variable” and “are” which refers to the plural it was in the previous version of the paper.
L.45. Cliff and Ord [9] is still not in the references.
Response to my comment 7 : “Our missing data model only considers the principle of missing data, that is, data missing at random, which is unrelated to whether it is endogenous.” is missing the point. If observations are missing depending on the dependent variable, then whether data are missing or not is still random but not “missing completely at random” and endogenous. Assumptions on missing data points should have been stated explicitly.
Comments on the Quality of English LanguageThe correct plural conjugation should be used
Author Response
We sincerely appreciate the detailed and conscientious feedback provided by the reviewers of the journal. Your insights and suggestions have been invaluable in guiding our revisions and improving the overall quality of our manuscript. We are truly grateful for the time and effort invested in reviewing our work. For a comprehensive response to your comments and the changes made to the manuscript, please see the attachment.
Author Response File: Author Response.pdf
Reviewer 4 Report
Comments and Suggestions for AuthorsThe paper has been improved but there are still several issues to be handled.
1. The number of authors has been increased, a new author appears, and the order of the rest of the authors has been changed.
2. The references are sometimes notated by number, eg. [1], some times with author and number, Cliff and Ord [9], some times with the name of the first author and number, sometimes with names of two authors and number, some times with first author and et. al, even if the authors are only two. A general rule for the references, can help the reader.
3. In Theorem 1 are assumed only part of the Assumptions. There is no explanation why the other Assumptions are need. Furthermore, there is no formalized proof of the Theorem 1.
4. In Appendix there are more Assumptions but in Theorem 1.1 are used only part of them. For both Theorems in Appendix there are no formalized proofs.
Comments on the Quality of English LanguageThe English can be improved.
Author Response
We sincerely appreciate the detailed and conscientious feedback provided by the reviewers of the journal. Your insights and suggestions have been invaluable in guiding our revisions and improving the overall quality of our manuscript. We are truly grateful for the time and effort invested in reviewing our work. For a comprehensive response to your comments and the changes made to the manuscript, please see the attachment.
Author Response File: Author Response.pdf
Round 3
Reviewer 1 Report
Comments and Suggestions for AuthorsThe changes are minimal and do not address earlier issues.
Simply adding "the data in this study are randomly missing, but not endogenous" does not address the issue and seems to contradict the Monte Carlo where missingness modeled in (3.2) includes Yi itself and so clearly endogenous
Comments on the Quality of English LanguageEnglish is fine.
Author Response
Dear Editor,
Thank you for providing us with valuable feedback, allowing us the opportunity to revise our manuscript. We are deeply appreciative of the reviewers' thorough assessments and the beneficial suggestions received. After carefully reviewing the comments, we have made detailed revisions to address the deficiencies in the original manuscript. The primary modifications are as follows: we adjusted the research methods in line with the reviewers' suggestions, enhancing the scientific rigor of our arguments. Additionally, we corrected some computational errors and revised the results presented in Tables 1, 2, 3, and 5 based on the new research methods. We have also updated the corresponding author's email address. We highly value the constructive comments from the reviewers and are sincerely grateful for the opportunity to improve our manuscript. We have submitted the revised manuscript along with a detailed response to the reviewers' comments, and kindly request your review. Thank you very much for your time and assistance. Wishing you success in your endeavors! For detailed modifications we have made, please see the attachment.
Author Response File: Author Response.pdf
Reviewer 4 Report
Comments and Suggestions for AuthorsThere are some strong points in your exposition. However, they are not properly presented.
I would like to specify that the spatial dependencies are very important, but the Assumptions 2.1.1-2.1.10 or in Appendix the Assumptions 1 - 9 do not help to handle the dependence issue. In practical aspect, the assumption is justified by the application and not by the theoretical restrictions. The relation with the missing data is also under question.
Author Response
Thank you very much for your comments; your questions are of great value to this article. Hypotheses 2.1.1-2.1.10 in this paper are based on the findings from Lee[1] and address issues of spatial dependency in spatial autoregressive models. Hypotheses 1-9 are adjustments made according to the content of our study, all aimed at addressing the problems posed in this paper, specifically the issue of parameter estimation in spatial autoregressive models with missing data and measurement errors. The relationship with missing data is also provided in the proof and discussion sections.
[1]Lee, L.F., 2004. Asymptotic Distributions of Quasi-Maximum Likelihood Estimators for Spatial Autoregressive Models. Econometrica 72, 1899–1925.
