Purpose

To solve the problem of simulation evaluation with small samples, a fresh approach of grey estimation is presented based on classical statistical theory and grey system theory. The purpose of this paper is to make full use of the difference of data distribution and avoid the marginal data being ignored.

Design/methodology/approach

Based upon the grey distribution characteristics of small sample data, the definition about a new concept of grey relational similarity measure comes into being. At the same time, the concept of sample weight is proposed according to the grey relational similarity measure. Based on the new definition of grey weight, the grey point estimation and grey confidence interval are studied. Then the improved Bootstrap resampling is designed by uniform distribution and randomness as an important supplement of the grey estimation. In addition, the accuracy of grey bilateral and unilateral confidence intervals is introduced by using the new grey relational similarity measure approach.

Findings

The new small sample evaluation method can realize the effective expansion and enrichment of data and avoid the excessive concentration of data. This method is an organic fusion of grey estimation and improved Bootstrap method. Several examples are used to demonstrate the feasibility and validity of the proposed methods to illustrate the credibility of some simulation data, which has no need to know the probability distribution of small samples.

Originality/value

This research has completed the combination of grey estimation and improved Bootstrap, which makes more reasonable use of the value of different data than the unimproved method.

中文翻译：

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基于灰度估计和改进bootstrap的小样本仿真评价

目的

针对小样本模拟评价问题，提出了一种基于经典统计理论和灰色系统理论的灰色估计新方法。本文的目的是充分利用数据分布的差异性，避免边缘数据被忽略。

设计/方法/方法

基于小样本数据的灰度分布特点，定义了灰色关联相似度的新概念。同时，根据灰色关联相似度测度，提出了样本权重的概念。基于灰度权重的新定义，研究了灰度点估计和灰度置信区间。然后通过均匀分布和随机性设计改进的Bootstrap重采样作为灰度估计的重要补充。此外，通过使用新的灰色关系相似性度量方法，引入了灰色双边和单边置信区间的准确性。

发现

新的小样本评价方法可以实现数据的有效扩展和丰富，避免数据过度集中。该方法是灰度估计和改进的Bootstrap方法的有机融合。通过几个例子证明了所提方法的可行性和有效性，说明了一些模拟数据的可信度，不需要知道小样本的概率分布。

原创性/价值

本研究完成了灰度估计和改进的Bootstrap相结合，比未改进的方法更合理地利用了不同数据的值。