Validity of dependent bootstrapping in finite populations Original Research Article

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.