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A modified bootstrap estimator for the mean of an asymmetric distribution
Author(s) -
Swanepoel J.W.H.,
BEER C.F. De
Publication year - 1993
Publication title -
canadian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.804
H-Index - 51
eISSN - 1708-945X
pISSN - 0319-5724
DOI - 10.2307/3315660
Subject(s) - mathematics , mean squared error , estimator , statistics , confidence interval , bias of an estimator , population mean , efficient estimator , minimum variance unbiased estimator , population , sample size determination , monte carlo method , consistent estimator , sample (material) , physics , medicine , environmental health , thermodynamics
A modified bootstrap estimator of the population mean is proposed which is a convex combination of the sample mean and sample median, where the weights are random quantities. The estimator is shown to be strongly consistent and asymptotically normally distributed. The small‐ and moderate‐sample‐size behavior of the estimator is investigated and compared with that of the sample mean by means of Monte Carlo studies. It is found that the newly proposed estimator has much smaller mean squared errors and also yields significantly shorter confidence intervals for the population mean.