Multivariate beta-kernel cumulative distribution function estimator

We propose a novel multivariate beta kernel estimator for cumulative distribution function (CDF) estimation. The asymptotic properties of the estimator are derived, proving that the optimal convergence rate of the mean integrated squared error is achieved. We examine its finite-sample performance through extensive simulations. The results demonstrate superior performance compared to the empirical distribution function and classical kernel estimators, particularly in reducing integrated squared error. Applications using real data are provided.