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Reviewer #1:
This paper considers strong convergence of rowwise negatively orthant dependent random variables. Although I did not check all the detailed proofs, I found the mathematics used here looks correct. However, the presentation style should be changed for a better readability. First of all, the title of Section 1 can be switched to Introduction and main result, where you can state motivation, history, definitions, regularity conditions, and main theorems. Then you create Section 2 for the proofs, where you put the preliminary results and proofs of theorems. Also, conditions (1.7)-(1.9) and (1.11)-(1.14) may be stated in the associated theorems. Since this is basically an extension of independent variables, the techniques used here might resemble those in earlier work. Thus some steps may be condensed without damaging the content.
Reviewer #2:
In this paper, the author studies the convergence of partial sums of rowwise NOD random variables. Although this paper is motivated by statistical application to reliability, this paper only considers a limit theorem, so the motive of this paper is a bit artificial for statisticians. This may be a weak point of this paper. To enrich the motivation and background on this subject, the author is required to cite more recent relevant results published in international journals.
The mathematics sounds correct, but many of proofs are standard arguments and some of them may be reduced. Overall, English in this article is fine, but the author can consult a native speaker. And give the full word of NA and the meaning of it. |
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