Nonparametric inference for P(X＜Y) with paired variables

José Arturo Montoya ； Francisco Javier Rubio

《Journal of Data Science》 12卷2期 (2014/04) Pp. 359-375

https://doi.org/10.6339/JDS.201404_12(2).0009

並列摘要

We propose two classes of nonparametric point estimators ofθ=P(X＜Y) in the case where (X, Y) are paired, possibly dependent, absolutely continuous random variables. The proposed estimators are based on nonparametric estimators of the joint density of (X, Y) and the distribution function of Z=Y-X. We explore the use of several density and distribution function estimators and characterise the convergence of the resulting estimators of θ. We consider the use of bootstrap methods to obtain confidence intervals. The performance of these estimators is illustrated using simulated and real data. These examples show that not accounting for pairing and dependence may lead to erroneous conclusions about the relationship between X and Y.

並列關鍵字

Bootstrap ； dependence ； density estimation ； distribution estimation ； stress-strength model