The First-Median Test: A Two-Sided Version of the Control Median Test

Gastwirth, Joseph L.

doi:10.2307/2284039

Cited by 34 publications

(7 citation statements)

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“…Similar remarks can be made for all these kinds of quantile test. Gart (1963) proposed an approximate X 2 -test against a two-sided alternative based on 2 (12V s + 1-11-1)2(2s+3) Gastwirth (1968) provided more details about the asymptotic distribution of the control median statistic and proposed a modification of the test that is better suited for the two-sided alternatives. As noted earlier, precedence tests sometimes have the advantage that they lead to an early termination of an experiment.…”

Section: Review Of Some Literaturementioning

confidence: 99%

Precedence Tests and Confidence Bounds for Complete Data: An Overview and Some Results

Chakraborti¹,

Laan²

1996

The Statistician

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SummaryAn overview of some nonparametric procedures based on precedence (or exceedance) statistics is given. The procedures include both tests and confidence intervals. In particular, the construction of some simple distribution-free confidence bounds for location difference of two distributions with the same shape is considered and some properties are derived. The asymptotic relative efficiency of an asymptotic form of the corresponding test relative to Wilcoxon's two-sample rank-sum test and the two-sample Student's t-test is given for various cases.Some K -sample problems are discussed where precedence type tests are useful, along with a review of the literature.

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Section: Review Of Some Literaturementioning

confidence: 99%

Precedence Tests and Confidence Bounds for Complete Data: An Overview and Some Results

Chakraborti¹,

Laan²

1996

The Statistician

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“…This proposition is an extension of the result in the paper of Gastwirth (1968). Thus, some adjustments are needed.…”

Section: Appendix: Proofsmentioning

confidence: 64%

Empirical Likelihood-Based Confidence Intervals for the Sensitivity of a Continuous-Scale Diagnostic Test with Missing Data

Wang

Qin

2014

Communications in Statistics - Theory and Methods

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In a continuous-scale diagnostic test, the receiver operating characteristic (ROC) curve is useful to evaluate the range of the sensitivity at the cut-off point that yields a desired specificity. Many current studies on inference of the ROC curve focus on the complete data case. In this paper, an imputation-based profile empirical likelihood ratio for the sensitivity, which is free of bandwidth selection, is defined and shown to follow an asymptotically scaled Chi-square distribution. Two new confidence intervals are proposed for the sensitivity with missing data. Simulation studies are conducted to evaluate the finite sample performance of the proposed intervals in terms of coverage probability. A real example is used to illustrate the new methods.

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“…Here W = number of times Y i > Xii i = 1, "', n, j = 1, "', m. Define Proof: From the same results of Gastwirth [2J,it follows that,under H 0,(Ta,T:) has a bivariate normal limiting distribution when a is the true parameter value. Asymptotically, the means are 0, the variances are 1 and the correlation is also 1.…”

Section: Is Symmetricmentioning

confidence: 86%