Applications of the representative points in statistical simulations

作者：Fang KaiTai^*; Zhou Min; Wang WenJun

来源：Science China Mathematics, 2014, 57(12): 2609-2620.

DOI：10.1007/s11425-014-4860-9

• bootstrap
• kernel density estimation
• normal distribution
• representative points
• resampling
• statistical simulation

The paper gives a new approach to statistical simulation and resampling by the use of number-theoretic methods and representative points. Resempling techniques take samples from an approximate population. The bootstrap suggests to use a random sample to form an approximate population. We propose to construct some approximate population distribution by the use of two kinds of representative points, and samples are taken from these approximate distributions. The statistical inference is based on those samples. The statistical inference in this paper involves estimation of mean, variance, skewness, kurtosis, quantile and density of the population distribution. Our results show that the new method can significantly improve the results by the use of Monte Carlo methods.

• 出版日期2014-12
• 单位中国科学院数学与系统科学研究院; 北京师范大学-香港浸会大学联合国际学院; 海南师范大学