It is a well-known result in probability that if Xis a random variable with a continuous distribution F, then  is uniformly distributed over the interval  This idea helps us to build new score functions to choose the regularization parameter of kernel distribution estimator. Two classes of selectors are considered: the indirect  class and the  class. Although all the methods work well, those in the  class seem more appealing because they appear to be more robust in the simulations. A small scale comparison study (by simulations) between the popular method of Bowman et al. [3] and the indirect  methods is carried out in the paper. An optimality result of the indirect  methods is given in the article.

kernel estimation, bandwidth selection, distribution function, order statistics.