The paper gives a new approach to statistical simulation and resampling by the use of numbertheoretic methods and representative points. Resempling techniques take samples from an approximate population. The bootstrap...The paper gives a new approach to statistical simulation and resampling by the use of numbertheoretic 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.展开更多
基金supported by the Special Research Foundation from the Chinese Academyof Sciencesthe Beijing Normal University-Hong Kong Baptist University United International College Research(Grant No.R201409)National Natural Science Foundation of China(Grant No.11261016)
文摘The paper gives a new approach to statistical simulation and resampling by the use of numbertheoretic 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.
