Alternative estimation procedures for Pr(X less than Y) in categorized data.

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

Biometrics

journal_title

Biometrics

authors

Simonoff JS,Hochberg Y,Reiser B

subject

Has Abstract

pub_date

1986-12-01 00:00:00

pages

895-907

issue

4

eissn

0006-341X

issn

1541-0420

journal_volume

42

pub_type

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