Asymptotics of Subsampling for Generalized Linear Regression Models under Unbounded Design

Round 1

Reviewer 1 Report

This paper establishes the  conditional and unconditional  asymptotic normalities of a  subsample-based estimator for a generalized linear regression coefficient  without requiring  the covaraite to be bounded.   It may contains something new in theory, however the presentation is not good.    Also there  are many typos or grammatical errors.  Below are some of them. 

1.  Condition (A6)  of Theorem 2 implies that  pi_i  are all equal to each other, which is absurd. 

2.   In the second paragraph of the introduction,   the reference [10]  namely  Jordan, Lee and Yang (2018)  is  irrelated to  subsampling. 

3.  In the beginning of 2.1,   what do you mean by "a collection convex loss function"? 

4.   In the paragraph below equation (2),    the  Inverted triangle is used  before  defined.  The two paragraphes above and below equation (2) do not read smooth.  

5. The  sentence above equation (5)  is  a bit repetitive.  Also the symbol of convergence in distribution is used before defined. 

Reviewer 2 Report

the paper entailed " Asymptotic of Subsampling for Generalized Linear Regression Models under Unbounded Design " the authors present

The optimal subsampling is a statistical methodology for generalized linear models 2 (GLMs) to make inference quickly about parameter estimation in massive data regression. Existing 3 literature only considers bounded covariates. In this paper, we obtain the asymptotic normality 4 of the subsampling M-estimator based on the Fisher information matrix. Then, we study the 5 asymptotic properties of subsampling estimators of unbounded GLMs with no natural links, 6 including conditional asymptotic properties and unconditional asymptotic properties

the paper well written no Comments about it except the language need to review with native speaker.