Relationships Between Uniformity, Aberration and Correlation in Regular Fractions 3s-1

Kai Tai Fang, Chang Xing Ma

Research output: Chapter in book/report/conference proceedingConference proceeding

Abstract

Uniformity has played a key role in quasi-Monte Carlo methods as well as in computer experiments. The minimum aberration is the most popular criterion in factorial designs. In this paper we extend the results of Fang and Mukerjee (2000) from regular fractions of two-level factorials to regular fractions 3s-1 of three-level factorials and establish a relationship between uniformity and aberration of regular fractions 3s-1. There are many minimum aberration fractions 3s-1 whose performances in statistical estimation may be different even though they are isomorphic to each other. Uniformity can be used as a criterion for comparing designs. A new concept of uniformly regular design is proposed. Construction of uniformly regular 3s-1 designs is studied. We show that the uniformly minimum aberration 3s-1 design has lower correlation and less confounding than the non-uniform one.
Original languageEnglish
Title of host publicationMonte Carlo and Quasi-Monte Carlo Methods 2000
Subtitle of host publicationProceedings of a Conference held at Hong Kong Baptist University, Hong Kong SAR, China, November 27 – December 1, 2000
EditorsKai Tai Fang, Harald Niederreiter, Fred J. Hickernell
PublisherSpringer Berlin Heidelberg
Pages215–231
Number of pages17
Edition1st
ISBN (Electronic)9783642560460
ISBN (Print)9783540427186
DOIs
Publication statusPublished - 22 Jan 2002
Externally publishedYes
Event4th International Conference on Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing, MCMQC 2000 - Hong Kong Baptist University, Hong Kong
Duration: 27 Nov 20001 Dec 2000
https://www.math.hkbu.edu.hk/mcqmc/MCQMC2000.html (Link to conference website)
https://link.springer.com/book/10.1007/978-3-642-56046-0 (Link to conference proceedings)

Conference

Conference4th International Conference on Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing, MCMQC 2000
Country/TerritoryHong Kong
Period27/11/001/12/00
Internet address

User-Defined Keywords

  • Fractional Factorial Design
  • Minimum Aberration
  • Design Versus
  • Identical Block
  • Incomplete Design

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