Permutation Methods [electronic resource] : A Distance Function Approach /

The introduction of permutation tests by R. A. Fisher relaxed the paramet­ ric structure requirement of a test statistic. For example, the structure of the test statistic is no longer required if the assumption of normality is removed. The between-object distance function of classical test statis­ tics based on the assumption of normality is squared Euclidean distance. Because squared Euclidean distance is not a metric (i. e. , the triangle in­ equality is not satisfied), it is not at all surprising that classical tests are severely affected by an extreme measurement of a single object. A major purpose of this book is to take advantage of the relaxation of the struc­ ture of a statistic allowed by permutation tests. While a variety of distance functions are valid for permutation tests, a natural choice possessing many desirable properties is ordinary (i. e. , non-squared) Euclidean distance. Sim­ ulation studies show that permutation tests based on ordinary Euclidean distance are exceedingly robust in detecting location shifts of heavy-tailed distributions. These tests depend on a metric distance function and are reasonably powerful for a broad spectrum of univariate and multivariate distributions. Least sum of absolute deviations (LAD) regression linked with a per­ mutation test based on ordinary Euclidean distance yields a linear model analysis which controls for type I error.

Bibliographic Details

Main Authors:	Mielke, Paul W. author., Berry, Kenneth J. author., SpringerLink (Online service)
Format:	Texto biblioteca
Language:	eng
Published:	New York, NY : Springer New York : Imprint: Springer, 2001
Subjects:	Statistics., Statistical Theory and Methods.,
Online Access:	http://dx.doi.org/10.1007/978-1-4757-3449-2
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