2007/11/18 by Xinjia Chen, Chen, Xinjia
Computer Science · Mathematics · #62D05 #62L12 #65C05 #FOS: Computer and information sciences #FOS: Mathematics #Machine Learning (cs.LG) #Probability (math.PR) #Statistics Theory (math.ST) #cs.LG #math.PR #math.ST #msc:62D05 #msc:62L12 #msc:65C05 #stat.TH
paper · pdf · doi:10.48550/arxiv.0711.2801
31 pages, 4 figures, added proofs
arxiv created 2007/12/02 · arxiv updated 2013/11/05
In this paper, we consider the nonasymptotic sequential estimation of means of random variables bounded in between zero and one. We have rigorously demonstrated that, in order to guarantee prescribed relative precision and confidence level, it suffices to continue sampling until the sample sum is no less than a certain bound and then take the average of samples as an estimate for the mean of the bounded random variable. We have developed an explicit formula and a bisection search method for the determination of such bound of sample sum, without any knowledge of the bounded variable. Moreover, we have derived bounds for the distribution of sample size. In the special case of Bernoulli random variables, we have established analytical and numerical methods to further reduce the bound of sample sum and thus improve the efficiency of sampling. Furthermore, the fallacy of existing results are detected and analyzed.