Problem in the paper of van Zwet

  • Context: Graduate 
  • Thread starter Thread starter victoriaabc
  • Start date Start date
  • Tags Tags
    Paper
Click For Summary
SUMMARY

The forum discussion centers on the paper "A note on contiguity and Hellinger distance" by J. Oosterhoff and W.R. van Zwet, specifically addressing the proof of asymptotic normality and the equivalence of conditions (3.2), (3.3) to (3.8)-(3.10) as stated in Loeve's book. Participants seek clarification on the derivation of these equivalences and inquire about examples that satisfy conditions (3.4)-(3.6) within the normality theorem. The discussion highlights the need for detailed understanding of the paper's notations and theorems.

PREREQUISITES
  • Familiarity with asymptotic normality in statistics
  • Understanding of the normal convergence theorem
  • Knowledge of Hellinger distance and its applications
  • Proficiency in mathematical notation and proofs
NEXT STEPS
  • Review Loeve's book on probability theory for insights on the normal convergence theorem
  • Study examples of asymptotic normality in statistical literature
  • Explore Hellinger distance applications in statistical convergence
  • Investigate the implications of conditions (3.4)-(3.6) in the context of normality theorems
USEFUL FOR

Statisticians, mathematicians, and researchers studying asymptotic properties in probability theory, particularly those interested in the nuances of normal convergence and Hellinger distance.

victoriaabc
Messages
2
Reaction score
0
Hi all,

Please help! I am reading the paper "A note on contiguity and Hellinger distance" by J. Oosterhoff and W.R. van Zwet. I have tons of questions. The following is just one of them.

Question 1: in their paper, when they prove the asymptotic normality they claim that according to an equivalent form of the normal convergence theorem (from Loeve's book) they can obtain that conditions (3.2) and (3.3) are equivalent to (3.8)-(3.10). Is there anyone know how they got there?

I am sorry that I am unable to type the formula down, there are too many notations. If anyone is familiar with this paper, could you please kindly help me out? Thank you very much.
 
Physics news on Phys.org
Why don't you scan the pages and post them as a .gif or .jpeg
 
WWGD said:
Why don't you scan the pages and post them as a .gif or .jpeg
Hi WWGD,

Thank you for your suggestion. Attached are the pages. I highlighted the part that I have problems. Besides my previous question, I am also wondering if there is any example satisfying those conditions (3.4)-(3.6) in their normality theorem? Anyone can give me a hint?

Thank you very much for all your help.
 

Attachments

  • Capture1.JPG
    Capture1.JPG
    39.5 KB · Views: 454
  • Capture2.JPG
    Capture2.JPG
    39 KB · Views: 430
  • Capture3.JPG
    Capture3.JPG
    46.7 KB · Views: 435
  • Capture4.JPG
    Capture4.JPG
    33.5 KB · Views: 480

Similar threads

MHB Solve Calculus Problem: Answers to d, e, f in Math Paper
  • · Replies 3 ·
Replies
3
Views
1K
Graduate Confused about the Purcell effect in a cavity
  • · Replies 2 ·
Replies
2
Views
3K
Graduate Interpreting a paper on spectral analysis
  • · Replies 3 ·
Replies
3
Views
1K
Graduate Proof of Seifert-Van Kampen Theorem
  • · Replies 2 ·
Replies
2
Views
3K
MHB Attempting to add logic mathematics to a college paper - need your input
  • · Replies 2 ·
Replies
2
Views
2K
Graduate Trying to reproduce the energy levels of a molecule from a paper
  • · Replies 5 ·
Replies
5
Views
2K
April Fool's Physics Papers 2026
  • · Replies 2 ·
Replies
2
Views
631
Graduate Question about a particular paper on categorical data
  • · Replies 1 ·
Replies
1
Views
1K
Graduate Solving Møller Energy Distribution Problem in Paper
  • · Replies 7 ·
Replies
7
Views
2K
Graduate Numerical Hartree Fock with Finite Difference Matrices for Helium
  • · Replies 4 ·
Replies
4
Views
3K