Open AccessComparison of the Bootstrap and Delta Method Variances of the Variance Estimator of the Bernoulli Distribution
Author(s) -
Ying Ying Zhang,
Teng Zhong Rong,
Man Man Li
Publication year - 2018
Publication title -
asian journal of probability and statistics
Language(s) - English
Resource type - Journals
ISSN - 2582-0230
DOI - 10.9734/ajpas/2018/v1i424547
Subject(s) - bernoulli's principle , estimator , mathematics , variance (accounting) , statistics , delta method , distribution (mathematics) , variance based sensitivity analysis , bias of an estimator , bernoulli trial , minimum variance unbiased estimator , analysis of variance , one way analysis of variance , mathematical analysis , physics , accounting , business , thermodynamics
It is interesting to calculate the variance of the variance estimator of the Bernoulli distribution. Therefore, we compare the Bootstrap and Delta Method variances of the variance estimator of the Bernoulli distribution in this paper. Firstly, we provide the correct Bootstrap, Delta Method, and true variances of the variance estimator of the Bernoulli distribution for three parameter values in Table 2.1. Secondly, we obtain the estimates of the variance of the variance estimator of the Bernoulli distribution by the Delta Method (analytically), the true method (analytically), and the Bootstrap Method (algorithmically). Thirdly, we compare the Bootstrap and Delta Methodsin terms of the variance estimates, the errors, and the absolute errors in three gures for 101 parameter values in [0, 1], with the purpose to explain the di erences between the Bootstrap and Delta Methods. Finally, we give three examples of the Bernoulli trials to illustrate the three methods.