Author | Mielke, Paul W. author |
---|---|

Title | Permutation Methods [electronic resource] : A Distance Function Approach / by Paul W. Mielke, Kenneth J. Berry |

Imprint | New York, NY : Springer New York : Imprint: Springer, 2001 |

Connect to | http://dx.doi.org/10.1007/978-1-4757-3449-2 |

Descript | XV, 353 p. 2 illus. online resource |

SUMMARY

The introduction of permutation tests by R. A. Fisher relaxed the parametยญ 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 statisยญ tics based on the assumption of normality is squared Euclidean distance. Because squared Euclidean distance is not a metric (i. e. , the triangle inยญ 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 strucยญ 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. Simยญ 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 perยญ mutation test based on ordinary Euclidean distance yields a linear model analysis which controls for type I error

CONTENT

1 Introduction -- 2 Description of MRPP -- 3 Further MRPP Applications -- 4 Description of MRBP -- 5 Regression Analysis, Prediction, and Agreement -- 6 Goodness-of-Fit Tests -- 7 Contingency Tables -- 8 Multisample Homogeneity Tests -- A Computer Programs -- A.1 Chapter 2 -- A.2 Chapter 3 -- A.3 Chapter 4 -- A.4 Chapter 5 -- A.5 Chapter 6 -- A.6 Chapter 7 -- A.7 Chapter 8 -- References

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Statistics
Statistical Theory and Methods