One-sample problem: Comparisons of tests and estimates
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.
KeywordsBivariate Normal Distribution Alternative Sequence Spatial Sign Distribution Case Noncentrality Parameter
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