基于自助法的小样本数据分析方法研究

Research on Data Analysis of Small Sample Based on Bootstrap Method

摘要:

自助法(Bootstrap)和随机加权法(Bayes Bootstrap)都是较好的处理小样本数据的方法,其无先验性,以及计算过程中只需要实际观测数据的优越性,使其广泛地应用于实际数据处理之中,后者的估计精度要更好些。但对连续情况而言,自助法的计算特性使得重抽样本局限在原始样本范围内,无法渐进于真实情况。文章基于自助法研究了用改进的样本经验分布函数来解决这个问题,并通过仿真算例说明方法的有效性。

Abstract:

Bootstrap method and Bayes Bootstrap method are all better methods to deal with the data of small sample, which are only dependent on the observation and don’t need other assumption. For these reasons, they are adopted generally, and the latter has the more precise. But as to the continuous function, the calculatingly characteristic of the Bootstrap method limits the range of the resample which comes from the original, so it will make the Bootstrap distribution departure from the genuine distribution. Therefore the improving empirical distruction function of sample was introduced to solve the problem, which was based on Bootstrap method. The emulation of example from the thesis proved the validity of the improving method.