The DOI matches its Crossref record; 8 of the 8 references it cites were found in a registry or an index.
The Efficiency of Some Nonparametric Competitors of the $t$-Test
Open accessAbstract
Consider samples from continuous distributions $F(x)$ and $F(x - \theta)$. We may test the hypothesis $\theta = 0$ by using the two-sample Wilcoxon test. We show in Section 1 that its asymptotic Pitman efficiency, relative to the $t$-test, never falls below 0.864. This result also holds for the Kruskal-Wallis test compared with the $F$-test, and for testing the location parameter of a single symmetric distribution. A number of alternative notions of asymptotic efficiency are compared in Section 2. In this connection, certain difficulties arise because power is not necessarily a convex function of sample size. As an alternative to the Pitman notion of asymptotic efficiency, we consider in Section 3 one based on the speed with which power at a fixed alternative tends to 1. In particular we obtain, for the sign test relative to the $t$ in normal populations, the limit as $n \rightarrow \infty$ of the sequence of power efficiency functions. It is noted that certain interchanges of limit passages are not always possible.
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Citations
Cites
Use of Ranks in One-Criterion Variance Analysis
Kruskal, W. H., & Wallis, W. A. (1952) · Journal of the American Statistical Association · doi:10.1080/01621459.1952.10483441 · Cited by 13,912
A Measure of Asymptotic Efficiency for Tests of a Hypothesis Based on the sum of Observations
Chernoff, H. (1952) · The Annals of Mathematical Statistics · doi:10.1214/aoms/1177729330 · Cited by 3,550
Introduction to Mathematical Probability
(1938) · Nature · doi:10.1038/141769d0 · Cited by 531
On the Asymptotic Efficiency of Certain Nonparametric Two-Sample Tests
Mood, A. M. (1954) · The Annals of Mathematical Statistics · doi:10.1214/aoms/1177728719 · Cited by 406
Noether, G. E. (1955) · The Annals of Mathematical Statistics · doi:10.1214/aoms/1177728593 · Cited by 282
Some Rank Order Tests which are most Powerful Against Specific Parametric Alternatives
Terry, M. E. (1952) · The Annals of Mathematical Statistics · doi:10.1214/aoms/1177729381 · Cited by 122
Asymptotic Behavior of Some Rank Tests for Analysis of Variance
Andrews, F. C. (1954) · The Annals of Mathematical Statistics · doi:10.1214/aoms/1177728658 · Cited by 86
Hoeffding, W. (1994) · Springer series in statistics · doi:10.1007/978-1-4612-0865-5_11 · Cited by 69
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Metadata
- Authors
- Hodges, J. L., & Lehmann, E. L.
- Venue
- The Annals of Mathematical Statistics
- Publisher
- Institute of Mathematical Statistics
- Published
- 1956-06
- Volume
- 27
- Issue
- 2
- Pages
- 324-335
- ISSN
- 0003-4851 (ISSN-L)
- OpenAlex
- W2171481228
- Cited by
- 587
- References
- 8
- FWCI
- 6.26
- Type
- journal article
- Language
- en
- Open access
- bronze
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