摘要： For competing risks data, it is of interest to estimate the sub-distribution function of a particular failure event, which is the failure probability in the presence of competing risks. However, if multiple failure events per subject are available, estimation procedures become challenging even for the bivariate case. In this paper, we consider nonparametric estimation of a bivariate sub-distribution function, which has been discussed in the related literature. Adopting a decision-theoretic approach, we propose a new nonparametric estimator which improves upon an existing estimator. We show theoretically and numerically that the proposed estimator has smaller mean square error than the existing one. The consistency of the proposed estimator is also established. The usefulness of the estimator is illustrated by the salamander data and mouse data. 出版者： New York: Elsevier Inc 出版日期： 2014-11 出處： Journal of Multivariate Analysis, 2014-11, Vol.132, p.229-241 資源來源： Elsevier ScienceDirect Journals 版權： 2014 Elsevier Inc. 版權： Copyright Taylor & Francis Group Nov 2014 識別號： ISSN: 0047-259X 識別號： EISSN: 1095-7243 識別號： DOI: 10.1016/j.jmva.2014.08.009 識別號： CODEN: JMVAAI
