Summary
Exact expressions and large-sample approximations are given for the nonparametric confidence intervals for a shift parameter A, which are obtained from the two-sample Wilcoxon test. These intervals are shown to have the same asymptotic efficiency relative to the standard confidence intervals for A as the Wilcoxon test has relative to Student’s 2-test. As a consequence of this result, a constant multiple of the length of the nonparametric intervals is shown to be a consistent estimator of the quantity 1/∫f 2 (x) dx.
Received February 26, 1963.
This research was done while the author was a Professor of the Adolph C. and Mary Sprague Miller Institute for Basic Research in Science, University of California, Berkeley.
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Keywords
- Consistent Estimator
- Shift Parameter
- Asymptotic Efficiency
- Standard Interval
- Normal Cumulative Distribution Function
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Reference
Lehmann, E. L. (1963). Asymptotically nonparametric inference: An alternative approach to linear models. Ann. Math. Statist. 34 1494–1506.
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Lehmann, E.L. (2012). Nonparametric Confidence Intervals for a Shift Parameter. In: Rojo, J. (eds) Selected Works of E. L. Lehmann. Selected Works in Probability and Statistics. Springer, Boston, MA. https://doi.org/10.1007/978-1-4614-1412-4_41
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DOI: https://doi.org/10.1007/978-1-4614-1412-4_41
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