One-sample problem: Comparisons of tests and estimates

Part of the Lecture Notes in Statistics book series (LNS, volume 199)


The efficiency and robustness properties of the tests and estimates are discussed. The estimates (the mean vector, the spatial median, and the spatial Hodges-Lehmann estimate) are compared using their limiting covariance matrices. The Pitman asymptotical relative efficiencies (ARE) of the spatial sign and spatial signed-rank tests with respect to the Hotelling’s T 2 are considered in the multivariate t distribution case. The tests using inner and outer standardizations are compared as well. Simulation studies and some analyses of real datasets are used to illustrate the difference between the estimates and between the tests.


Bivariate Normal Distribution Alternative Sequence Spatial Sign Distribution Case Noncentrality Parameter 


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Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.Tampere School of Public HealthUniversity of TampereTampereFinland

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