Consistency and Accuracy of The Bootstrap Estimator for Mean Under Kolmogorov Metric

Suprihatin, Bambang and Guritno, Suryo and Haryatmi, Sri (2012) Consistency and Accuracy of The Bootstrap Estimator for Mean Under Kolmogorov Metric. The 6th SEAMS-GMU 2011 International Conference on Mathematics and Its Applications. pp. 679-688. ISSN 978-979-17979-3-1

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Abstract

It is known that by Strong Law of Large Number, the sample mean converges almost surely to the population sample . Central Limit Theorem asserts that the distribution of converges to Normal distribution with mean 0 and variance as . In bootstrap view, the key of bootstrap terminology says that the population is to the sample as the sample is to the bootstrap samples. Therefore, when we want to investigate the consistency of the bootstrap estimator for sample mean, we investigate the distribution of contrast to , where is bootstrap version of computed from sample bootstrap . Asymptotic theory of the bootstrap sample mean is useful to study the consistency for many other statistics. Thereupon some authors call as pivotal statistic. Here are two out of some ways in proving the consistency of bootstrap estimator. Firstly, the consistency was under Mallow-Wasserstein metric (Bickel and Freedman, 1981). The other consistency is using Kolmogorov metric, which is a part of paper in Singh (1981). DasGupta (2008) also discussed this topic. In this our paper, we investigate the consistency under Kolmogorov metric comprehensively. The accuracy of the bootstrap estimator using Edgeworth expansion is discussed as well. Results of simulations show that the bootstrap gives good estmates of standard error, which agree to the theory. All results of Monte Carlo simulations are also presented in regard to yield apparent conclusions.

Item Type:	Article
Subjects:	Q Science > QA Mathematics > QA1-939 Mathematics > QA21 Calculus. MATHEMATICS
Divisions:	08-Faculty of Mathematics and Natural Science > 44201-Mathematics (S1)
Depositing User:	Mr Bambang Suprihatin
Date Deposited:	11 Dec 2019 06:16
Last Modified:	11 Dec 2019 06:16
URI:	http://repository.unsri.ac.id/id/eprint/21208

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