Nonparametric Probability Density Function Estimation Using the Padé Approximation
Round 1
Reviewer 1 Report
Comments and Suggestions for Authors
see attached file
Comments for author File: 
Comments.pdf
Author Response
We thank the reviewers for their careful review and constructive suggestions. Please see our detailed responses attached.
Author Response File: Author Response.pdf
Reviewer 2 Report
Comments and Suggestions for Authors
The paper considers an algorithm for improving the estimation of probability density using Pade approximation. In the introduction, the authors of the article elaborated on various applications of this problem and on publications that have been developing algorithms for estimating probability density in recent years. Judging by these links, further progress in this direction has slowed down somewhat in the last five years (there are only three references in the list of references). Apparently, this circumstance required the authors to use a more subtle computational approximation tool in addition to the method of moments. I liked that the authors used the densities of classical distributions Gaussian Mixture, Exponential Distribution, and Gamma Distribution as examples of the application of their proposed method. For statisticians, these are quite significant examples. In Tables 1-6, as well as in Figures 1-8, especially when contrasting Figures 1, 2 to Figure 3, the advantages of using the authors' method are convincingly demonstrated. These figures and tables primarily indicate the accuracy of the approximations obtained by the authors using several probability distances, which makes the results more convincing for statisticians. The authors drew attention to the task of processing small samples, which is very sensitive for approximations of probability density, and showed the advantages of their method in this part. But I would like to draw the authors' attention to the need to evaluate the computational complexity of their proposed algorithms. In general, the paper deserves to be published in the journal Algorithms after minor clarifications.
Author Response
We thank the reviewers for their careful review and constructive suggestions. Please see our detailed responses attached.
Author Response File: Author Response.pdf
Reviewer 3 Report
Comments and Suggestions for Authors
The work is of interest to the journal. However, some shortcomings of the work should be eliminated before its publication.
1 When proving the relevance of the research, the authors refer to little-known works that are proceedings and abstracts of conferences. [1-4], for example. I would like to see basic research that supports your position.
2 Source [5] is dated 1949. A lot of new knowledge and developments have been gained during this time. The authors write (lines 36-37): ‘Such estimation is always valuable, but it is nonetheless challenging [5], especially when the available data are limited’. However, what was difficult in 1949 before the use of computer technology could be simple today. The reference [5] in the context of the sentence looks very unconvincing.
3 The authors write (lines 117-118): ‘Amindavar and Ritcey first proposed the use of the Padé approximation for estimating PDFs’. Provide a reference to their work.
4 The authors write (lines 120-124): ‘First, the method is only applicable to strictly positive data. Second, the method exhibits substantial distortion on the left side of the approximated PDF. Third, the original method did not demonstrate accurate PDF modelling when moments must be estimated directly from sample data’. Indicate by whom these deficiencies were identified and where they are described.
Author Response
We thank the reviewers for their careful review and constructive suggestions. Please see our detailed responses attached.
Author Response File: Author Response.pdf
Round 2
Reviewer 1 Report
Comments and Suggestions for Authors
see attachment
Comments for author File: Comments.txt
