Abstract:
:Consider two independent random variables X and Y. The functional R = Pr(X less than Y) [or gamma = Pr(X less than Y) - Pr(Y less than X)] is of practical importance in many situations, including clinical trials, genetics, and reliability. In this paper several approaches to estimation of gamma when X and Y are presented in discretized (categorical) form are analyzed and compared. Asymptotic formulas for the variances 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 gamma, 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.
journal_name
Biometricsjournal_title
Biometricsauthors
Simonoff JS,Hochberg Y,Reiser Bsubject
Has Abstractpub_date
1986-12-01 00:00:00pages
895-907issue
4eissn
0006-341Xissn
1541-0420journal_volume
42pub_type
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