Abstract #301849

This is the preliminary program for the 2003 Joint Statistical Meetings in San Francisco, California. Currently included in this program is the "technical" program, schedule of invited, topic contributed, regular contributed and poster sessions; Continuing Education courses (August 2-5, 2003); and Committee and Business Meetings. This on-line program will be updated frequently to reflect the most current revisions.

To View the Program:
You may choose to view all activities of the program or just parts of it at any one time. All activities are arranged by date and time.

The views expressed here are those of the individual authors
and not necessarily those of the ASA or its board, officers, or staff.

Back to main JSM 2003 Program page
JSM 2003 Abstract #301849
Activity Number: 469
Type: Contributed
Date/Time: Thursday, August 7, 2003 : 10:30 AM to 12:20 PM
Sponsor: IMS
Abstract - #301849
Title: Infinitely Divisible Approximations for Nonparametric i.i.d. Experiments
Author(s): Harrison Huibin Zhou*+ and Michael Nussbaum
Companies: Cornell University and Cornell University
Address: Department of Mathematics, Ithaca, NY, 14850,
Keywords: infinitely divisible experiments ; nonparametric density classes ; deficiency distance ; endpoint ; order statistic ; tail rate
Abstract:

The asymptotic equivalence of density estimation and Gaussian white noise has been established in Nussbaum (1996), where for the nonparametric class of densities a common support [0,1] is assumed. The question we pose here is, Can the condition "bounded away from zero'' be weakened or removed? It can be seen that if an additional location parameter is introduced, then the Gaussian white noise approximation fails. This paper shows that the correct approximation in this case is an infinitely divisible experiment that is a Gaussian/Poisson mixture. In analogy to results for endpoint estimation, the tail rates of the densities are crucial for the shape of the approximation. A theory of infinitely divisible experiments has been developed in the monograph of Janssen, Milbrodt and Strasser (1985), with a view to parametric models and local limits. Our focus here is on nonparametric i.i.d models and global asymptotic equivalence.

  • The address information is for the authors that have a + after their name.
  • Authors who are presenting talks have a * after their name.

Back to the full JSM 2003 program

JSM 2003 For information, contact meetings@amstat.org or phone (703) 684-1221. If you have questions about the Continuing Education program, please contact the Education Department.
Revised March 2003