Validity of dependent bootstrapping in finite populations

The traditional bootstrap resamples with replacement from the original sample observations to form arrays of row-wise independent and identically distributed bootstrap random variables. There are situations, for example, when sampling from finite populations, where resampling without replacement pro...

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Bibliographic Details
Published inNonlinear analysis Vol. 71; no. 12; pp. e1021 - e1032
Main Authors Taylor, Robert L., Smith, Wendy D.
Format Journal Article
LanguageEnglish
Published Elsevier Ltd 15.12.2009
Subjects
Bootstrapping
Central limit theorem
Conditional convergence in distribution
Consistency
Negative associated
Negative dependent
Validity
Bootstrapping
Validity
Negative dependent
Central limit theorem
62G09
Conditional convergence in distribution
62E20
Consistency
Negative associated
60F05
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Summary:The traditional bootstrap resamples with replacement from the original sample observations to form arrays of row-wise independent and identically distributed bootstrap random variables. There are situations, for example, when sampling from finite populations, where resampling without replacement provides a more realistic bootstrap procedure and produces dependent bootstrap random variables. The desired properties of consistency and asymptotic validity are shown to hold for certain nonparametric dependent bootstrap estimators. In addition, it is shown that the smaller variation in dependent bootstrap estimators can be used to increase precision in some of the estimators.
ISSN:0362-546X
1873-5215
DOI:10.1016/j.na.2009.01.072