Abstract
As statistical estimation procedures for location, the sample mean, Hodges and Lehman's R-estimator, and Huber's M-estimator are introduced in a one-sample model. The asymptotic distributional theory for the three estimators and simulated mean squared errors give the features of the respective estimators depending on the underlying distribution. Based on the features, we propose an estimation procedure selecting one of the three estimators after searching a distribution near to the underlying distribution. It is shown that the mean squared error of the new estimator is more stable than the three estimators.Next, as distribution-free test procedures, the conditional t-test, Wilcoxon's signed rank test, and the M-test are introduced. Asymptotic relative efficiency and simulated power of the respective tests are investigated. Based on their features, we propose a stable test procedure selecting one of the three tests after searching a distribution near to the underlying distribution.
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