A Penalized Empirical Likelihood Approach for Estimating Population Sizes under the Negative Binomial Regression Model

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

Paper is devoted to application of negative binomial regression model in data with overdispersion and heterogeneity.

In section 2 authors presented in detail negative binomial regression mode with penalized empirical likelihood estimation approach. Also they define the EM algorithm.  The main result in the article is Theorem 1. The proof of this result is presented in Appendix.

Section 3 includes some simulations that have the aim to illustrate how the proposed methods can be applied. Also there are analyze of multiple synthetic data sets.

Section 4 is practical with real data for the black bear in New York. The experiment is presented in detail. The paper ends with conclusion and discussion.

The presented article is interesting with detailed discussions. It will be interesting to reader to presented some comparing with other models or algorithms.  One more real data set with some graphics should be added.

Introduction section should contain mainly description of the problem. In the conclusion describe how the problem is solved.

One suggestion: it is not suitable to add reference before definition, it is difficult to reader to go ahead to see definition and return back. For example (1) is defined in line 85, but it is cited in line 38.  My opinion is that the proof of Theorem 1 should be in the text, not in the appendix.  Also in line 114 cite (3) without word Equation. There are some formulas in two lines, for example see lines 119, 155, 378, 382 and others.

 

 

 

Comments on the Quality of English Language

Minor editing of English language required.

Author Response

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Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

Please find my comments attached.

Comments for author File: Comments.pdf

Author Response

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Author Response File: Author Response.pdf

Reviewer 3 Report

Comments and Suggestions for Authors

The paper addresses the challenges in capture-recapture experiments where overdispersion and heterogeneity necessitate the use of the negative binomial regression model for estimating population sizes. Existing methods for estimating the dispersion parameter often lead to unrealistic results, such as excessively large point estimates and unbounded confidence intervals. To overcome these issues, the paper proposes a penalized empirical likelihood technique that imposes a half-normal prior on the population size. According to the authors, this approach yields more reliable and efficient estimates, supported by an expectation-maximization (EM) algorithm to improve numerical performance. Based on simulation experiments, they also showed that the proposed method effectively resolves boundary problems and provides more precise interval estimates.

Shortcoming(s):

+Some language issues especially in grammar must be revised: for instance:

    - L 38, "as defined in (1) in Section 2.1" can be " of section"

    - L 49,  "may be not reliable" should be "may not be reliable."

     - etc
+L 423, reference is missing
+ For clarity, the algorithms can be presented in pseudocode. This approach will allow readers to easily follow the step-by-step logic and structure of the algorithms, enhancing their understanding of the methodology.

Author Response

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Author Response File: Author Response.pdf

Reviewer 4 Report

Comments and Suggestions for Authors

Please see in pdf-file.

Comments for author File: Comments.pdf

Author Response

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Author Response File: Author Response.pdf

Round 2

Reviewer 2 Report

Comments and Suggestions for Authors

The authors addressed all my comments. I do not have further comments at this time. Thanks.

Reviewer 4 Report

Comments and Suggestions for Authors

I am saisfied with the revised paper. It can be published.