小样本下分位数函数的Bootstrap置信区间估计

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小样本下分位数函数的Bootstrap置信区间估计

袁修开¹, 吕震宙¹, 岳珠峰²

1. 西北工业大学航空学院, 陕西西安 710072;
2. 西北工业大学力学与土木建筑学院, 陕西西安 710072

收稿日期:2011-11-01 修回日期:2011-11-22 出版日期:2012-10-25 发布日期:2012-10-25
通讯作者: 吕震宙 E-mail:zhenzhoulu@nwpu.edu.cn
基金资助:
国家自然科学基金(51175425, 51105309);航空科学基金(2011ZA53015);中国博士后科学基金(2011M501470)

Bootstrap Confidence Interval of Quantile Function Estimation for Small Samples

YUAN Xiukai¹, LU Zhenzhou¹, YUE Zhufeng²

1. School of Aeronautics, Northwestern Polytechnical University, Xi’an 710072, China;
2. School of Mechanics, Civil Engineering & Architecture, Northwestern Polytechnical University, Xi’an 710072, China

Received:2011-11-01 Revised:2011-11-22 Online:2012-10-25 Published:2012-10-25
Supported by:
National Natural Science Foundation of China (51175425, 51105309); Aeronautical Science Foundation of China(2011ZA53015); China Postdoctoral Science Foundation (2011M501470)

摘要/Abstract

摘要： 航空产品试验一般为小样本试验,为了分析小样本情况下的试验数据,结合以概率加权矩为约束条件的最大熵法和求解置信区间及置信带的Bootstrap方法,提出了一种估计小样本试验件母体分位数函数置信区间的方法。最大熵法在矩约束下能够估计样本的密度函数,而以概率加权矩为约束条件的最大熵法能够针对小样本直接给出分位数的无偏估计,无需由密度函数积分得到累积分布函数,再进行转化得到分位数函数。Bootstrap方法求解置信区间具有不依赖于数据分布的优点,具有广泛的应用范围。

关键词: 分位数, 置信区间, 最大熵法, 概率加权矩, Bootstrap方法

Abstract: The tests of aeronautic products are usually small sample cases. In order to analyze the data of small sample tests, a confidence interval estimation method for test population sample quantile function is proposed by combining the maximum entropy method under probability-weighted moment constraints and the Bootstrap method for confidence interval estimation. The maximum entropy method can yield the probability density function under specified moment constraints. When it is subjected to the constraints specified in terms of probability-weighted moment, an unbiased quantile estimate for small samples can be directly obtained. There is no need to integrate form density function to obtain cumulative distribution function which has then to be inverted to obtain the corresponding quantile. The Bootstrap method not only is independent of the distribution of samples in the estimation of the confidence interval but also has wide applications.

Key words: quantile, confidence interval, maximum entropy methods, probability-weighted moment, Bootstrap method

中图分类号:

袁修开, 吕震宙, 岳珠峰. 小样本下分位数函数的Bootstrap置信区间估计[J]. 航空学报, 2012, 33(10): 1842-1849.

YUAN Xiukai, LU Zhenzhou, YUE Zhufeng. Bootstrap Confidence Interval of Quantile Function Estimation for Small Samples[J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2012, 33(10): 1842-1849.

参考文献

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E-mail：hkxb@buaa.edu.cn

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主管单位：中国科学技术协会主办单位：中国航空学会北京航空航天大学

小样本下分位数函数的Bootstrap置信区间估计

Bootstrap Confidence Interval of Quantile Function Estimation for Small Samples

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