Inference Based on Simple Step Statistics for the Location Model.
PENNSYLVANIA STATE UNIV UNIVERSITY PARK DEPT OF STATISTICS
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Until recent years, statistical theory has emphasized optimal procedures under an assumed underlying model. However, these methods may be highly sensitive to slight departures from the model assumptions non-robust, and they may be inferior to other procedures for these alternative models inefficient. The sample mean is an example of an estimator which suffers from these criticisms. In this paper, a class of estimation procedures which are robust, relatively efficient, and yet computationally simple is proposed for the one- and two-sample location problems. Particular emphasis is placed on the problems of determining confidence intervals with the properties stated above, a topic which has seen limited exposure in the literature. As a by-product, some interesting point estimates are obtained. A class of score functions which are ordinary step functions is considered for the location model. Point estimates and confidence intervals are obtained by inverting the corresponding rank statistics. Efficiency and robustness properties of the procedures are investigated. Several computational schemes are illustrated which make the estimates and confidence intervals quite easy to compute. Author
- Statistics and Probability