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Alternative Estimation Procedures for Pr(X < Y) in Categorized Data
Jeffrey S. Simonoff, Yosef Hochberg and Benjamin Reiser
Vol. 42, No. 4 (Dec., 1986), pp. 895-907
Published by: International Biometric Society
Stable URL: http://www.jstor.org/stable/2530703
Page Count: 13
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Consider two independent random variables X and Y. The functional R = Pr(X < Y) [or λ = Pr(X < Y) - Pr(Y < X)] is of practical importance in many situations, including clinical trials, genetics, and reliability. In this paper several approaches to estimation of λ when X and Y are presented in discretized (Categorical) form are analyzed and compared. Asymptotic formulas for the variance of the estimators are derived; use of the bootstrap to estimate variances is also discussed. Computer simulations indicate that the choice of the best estimator depends on the value of λ, the underlying distribution, and the sparseness of the data. It is shown that the bootstrap provides a robust estimate of variance. Several examples are treated.
Biometrics © 1986 International Biometric Society