Abstract
The t-statistic computed as a function of the scores of a two-sampie linear rank statistic, rather than the observations them-selves, yields a statistic TCR which can be used to test for the equality of locations of two populations. For the Wilcoxon scores, the statistic TcR reduces to the f, rank transform” statistic T. By assuming the appropriate regularity conditions on the scores, TCR is shown to have approximately a t-distribution. The asymptotic relative efficiency (ARE) of T is the same as that of the corre-CR sponding linear rank statistic. The robustness of TCR, with respect to significance level and power, is studied by Monte Carlo simulation when the distributions are normal, uniform, double exponential Cauchy, and exponential.
| Original language | English |
|---|---|
| Pages (from-to) | 1437-1455 |
| Number of pages | 19 |
| Journal | Communications in Statistics - Theory and Methods |
| Volume | 10 |
| Issue number | 14 |
| DOIs | |
| State | Published - Jan 1 1981 |
| Externally published | Yes |
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All Science Journal Classification (ASJC) codes
- Statistics and Probability
Cite this
A Generalization of the Rank Transform in the Two-Sample Location Problem. / Nath, Ravinder; Duran, B. S.
In: Communications in Statistics - Theory and Methods, Vol. 10, No. 14, 01.01.1981, p. 1437-1455.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - A Generalization of the Rank Transform in the Two-Sample Location Problem
AU - Nath, Ravinder
AU - Duran, B. S.
PY - 1981/1/1
Y1 - 1981/1/1
N2 - The t-statistic computed as a function of the scores of a two-sampie linear rank statistic, rather than the observations them-selves, yields a statistic TCR which can be used to test for the equality of locations of two populations. For the Wilcoxon scores, the statistic TcR reduces to the f, rank transform” statistic T. By assuming the appropriate regularity conditions on the scores, TCR is shown to have approximately a t-distribution. The asymptotic relative efficiency (ARE) of T is the same as that of the corre-CR sponding linear rank statistic. The robustness of TCR, with respect to significance level and power, is studied by Monte Carlo simulation when the distributions are normal, uniform, double exponential Cauchy, and exponential.
AB - The t-statistic computed as a function of the scores of a two-sampie linear rank statistic, rather than the observations them-selves, yields a statistic TCR which can be used to test for the equality of locations of two populations. For the Wilcoxon scores, the statistic TcR reduces to the f, rank transform” statistic T. By assuming the appropriate regularity conditions on the scores, TCR is shown to have approximately a t-distribution. The asymptotic relative efficiency (ARE) of T is the same as that of the corre-CR sponding linear rank statistic. The robustness of TCR, with respect to significance level and power, is studied by Monte Carlo simulation when the distributions are normal, uniform, double exponential Cauchy, and exponential.
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UR - http://www.scopus.com/inward/citedby.url?scp=84948243996&partnerID=8YFLogxK
U2 - 10.1080/03610928108828125
DO - 10.1080/03610928108828125
M3 - Article
VL - 10
SP - 1437
EP - 1455
JO - Communications in Statistics - Theory and Methods
JF - Communications in Statistics - Theory and Methods
SN - 0361-0926
IS - 14
ER -