小样本下分位数函数的Bootstrap置信区间估计

ACTA AERONAUTICAET ASTRONAUTICA SINICA ›› 2012, Vol. 33 ›› Issue (10): 1842-1849.

• Solid Mechanics and Vehicle Conceptual Design • Previous Articles Next Articles

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)

Abstract

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

CLC Number:

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.

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Bootstrap Confidence Interval of Quantile Function Estimation for Small Samples

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