AI Article Synopsis
- The study focuses on estimating the probability that one independent random variable (X) is less than another (Y), which is crucial in fields like clinical trials and genetics.
- Different methods for estimating this probability when the variables are in categorical form are analyzed and compared, particularly how each method's variance behaves.
- Simulation results suggest that the best estimation method varies based on the actual value of the probability, the distribution of the data, and how sparse the dataset is, with the bootstrap method being particularly effective for variance estimation.
Article 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.
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