Schmerling S, Peil J, Kupper H
Gegenbaurs Morphol Jahrb. 1984;130(6):779-92.
A nonparametric method for estimation of one-dimensional continuous probability distribution functions is presented. Procedures for calculation of estimation of the unknown distribution function and the distribution density will be discussed in their application. 2 items are what type of weight function may be chosen for the proposed local-linear continuous approximation of the empirical distribution function by the least squares method (LOLINREG), and upon what value of bandwidth- or smoothing parameter one optimally should settle. The latter problem is practically very important with respect to the quality of the estimation results. Examples of simulated measurements which come from a standardized normal distribution as random numbers serve to demonstrate the mode of working, the advantages as well as the limits of the presented continuous LOLINREG-approximation.
提出了一种用于估计一维连续概率分布函数的非参数方法。将在其应用中讨论计算未知分布函数和分布密度估计的程序。有两个问题，一是对于所提出的通过最小二乘法对经验分布函数进行局部线性连续逼近（LOLINREG）可以选择何种类型的权重函数，二是最优地应确定带宽或平滑参数的何种值。后一个问题对于估计结果的质量在实际中非常重要。来自标准化正态分布的模拟测量示例作为随机数用于展示所提出的连续LOLINREG逼近的工作方式、优点以及局限性。
