A Review of Nonparametric Research on Cumulative Distribution Function Estimation

This paper intends to review non-parametric studies on estimating the cumulative distribution function (CDF) of a random variable. Research in this field has mostly utilized kernel-type methods. Generally, studies on estimating CDF by kernel methods can be grouped into three categories, including the studies on the conditions and convergence rate of the estimator, studies on how to select the estimator’s smoothing parameter, and studies on boundary problem-solving. We also consider the CDF estimation for the multivariate and the conditional cases as well as CDF for time series and dependent data. Our approach, however, is not merely a review of these studies. Whenever possible, we have analyzed and compared the strengths and weaknesses of various methods proposed by the researchers.