Density Estimation with Bivariate Censored Data
针对随机删失的双变量数据，构造了核密度估计量，证明了其大样本性质（一致性和渐近正态性），并通过模拟验证了中等样本量下的良好表现，讨论了带宽选择和边界效应等实现问题。
Abstract In this article we construct a kernel estimate of the probability density function from bivariate data that have been randomly censored. We study the large-sample properties of the proposed estimator using a strong approximation result. We establish consistency and asymptotic normality and give a convenient representation of the kernel density estimator. Simulation studies show that the proposed procedure gives a good estimate of the true density function even when the sample size is moderate. We discuss various issues about implementation of the estimator, including bandwidth selection and boundary effects. The procedure can be generalized to higher dimensional variables in a straightforward manner. Key Words: Bivariate failure time dataKernel density estimationStrong approximationSurvival analysis