Rigorous error control methods for estimating means of bounded random variables

• Published in: Journal of statistical planning and inference Vol. 157-158; pp. 54 - 76
• Main Authors: Chen, Zhengjia, Chen, Xinjia
• Format: Journal Article
• Language: English
• Published: Netherlands Elsevier B.V 01.02.2015
• Subjects: Bounded random variable; Mean estimation; Rigorous error control method; Mean estimation; Rigorous error control method; Bounded random variable
• ISSN: 0378-3758; 1873-1171
• DOI: 10.1016/j.jspi.2014.08.007

In this article, we propose rigorous sample size methods for estimating the means of random variables, which require no information of the underlying distributions except that the random variables are known to be bounded in a certain interval. Our sample size methods can be applied without assuming that the samples are identical and independent. Moreover, our sample size methods involve no approximation. We demonstrate that the sample complexity can be significantly reduced by using a mixed error criterion. We derive explicit sample size formulae to ensure the statistical accuracy of estimation. •A rigorous sample size method for estimating the means of bounded random variables.•It requires neither information nor IID condition of the underlying distribution.•It involves no approximation.•Sample complexity can be significantly reduced by using a mixed error criterion.•Explicit sample size formulae to ensure the statistical accuracy of estimation.