A New Class of Bayes Minimax Estimators of the Mean Matrix of a Matrix Variate Normal Distribution

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

1.  The abstract is too simple, more content and details are needed.

2.  Line 54. "In this note" should be revised to "In this paper". This issue also comes up several times in the later text and needs to be revised.

3.  Line 73 and 74.  Whether V in Vm,p = { V ∈ R m×p , V′V = Ip } and V in V ∈ Vm,p have the same meaning? If not, use another symbol for V in line 74.

4.  Line 116. g(·) is a decreasing function. From the beginning of Section 2, the reviewer does not find out the expression of g(·).

5.  Line 104 and 122, ∧ has two different meanings in the paper. One is a variable in line 104, the other is an operator in line 122.

6.  Line 179.  g'(t) < 0, not g'(t) <= 0.

7.  Line 185.  What is the meaning of "g(1^{-1})" ?

Author Response

Please see attached.

 

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

This is a good paper, but I have some questions and suggestions:

 

1. Introduction:

The authors begin by discussing the "matrix variate normal distribution," indicating its widespread use across various fields. However, I believe the approach is not quite accurate, as it first diverts attention to defining what a "matrix variate normal distribution" is and then stating its extensive application. While the authors do define a matrix of this type in line 29, why not start the paragraph in this way?

 

A similar issue arises with the "Bayes minimax estimation," as the discussion commences with the case "m>p+1," but it's unclear what this "Bayes minimax" entails. Who are "m" and "p"?

2. A class of Bayes minimax estimators of the mean matrix 

The authors begin their discussion with the "matrix variate normal distribution," noting its application in numerous fields. However, I believe the approach might not be the most appropriate. Initially, it is essential to define what a "matrix variate normal distribution" is before highlighting its extensive use. In line 29, the authors define a matrix of this type, so why not start the paragraph with this explanation?

 

The section on "Bayes minimax estimation" encounters a similar issue. It begins by discussing the case "m > p + 1," but it remains unclear what the "Bayes minimax" actually involves. Who are "m" and "p"?

 

3. Examples

 

As with the previous case, separating the paragraphs could enhance reader comprehension.

 

EXAMPLE 1 is somewhat unclear... I'm not sure... it doesn't fully illustrate the exact function being proposed.

 

In Example 2, a similar issue arises; the final result is not entirely clear. Who are the "Bayes estimators obtained"?

 

 

4. Concluding remarks

I am having trouble understanding this section. One would expect a set of conclusions where the proposed estimators are compared with existing ones to understand the novelty of the subject, but this comparison is nowhere to be found in the article.

Author Response

Please see attached.

 

Author Response File: Author Response.pdf

Reviewer 3 Report

Comments and Suggestions for Authors

This paper needs a major revision and satisfactory answers to my queries before I can process it further. Attached please find my comments from the preliminary reading of the manuscript

 

Comments for author File: Comments.pdf

Author Response

Please see attached.

 

Author Response File: Author Response.pdf

Round 2

Reviewer 2 Report

Comments and Suggestions for Authors

In the compilation proces the bibliography fail. Please re-compile correctly. By the other hand. I kown that is a theoretical paper, but, I have the same question that in the first version. Where could use this approach?  The two presented examples need better introduction. 

And for the conclussions remarks, again my question is: A simulation study is needed in order to view the adventages of this new proposal.

Author Response

Please see attached.

 

Author Response File: Author Response.pdf

Reviewer 3 Report

Comments and Suggestions for Authors

The authors may look into the 2022 book on " Multivariate Statistical Analysis in the Real and Complex Domains", Springer Nature, Switzerland. It will help the authors to evaluate the conditional moment in the current paper and for for future work. The authors did not really answer my main comment, the same thing is rephrased in the revised version. I am recommending the paper for publication because all those steps are not needed to evaluate the expected value. The above mentioned book will help in evaluating the expected value explicitly and directly.

In the revised version, insert all the missing equation numbers in the text. Also in the Introduction lines 1,5 replace "random matrix" by matrix random variable (In other disciplines, random matrix is used with a different interpretation as row sums being 1 etc.). Also, replace "multivariate statistics" by "multivariate statistical analysis"

Author Response

Please see attached.

 

Author Response File: Author Response.pdf