Inequalities and bounds for kernel length-biased density estimation

摘要

In this note non-parametric estimates of the length-biased probability density function and related reliability measures are presented. Non-parametric estimates are also presented under random censoring. Inequalities and bounds for the error of kernel estimators used for the estimation of length-biased probability densities are obtained. Non-asymptotic bounds and stochastic convergence results are established. Inference for length-biased energy functions is developed and implemented.