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A new resampling method for sampling designs without replacement: the doubled half bootstrap
A new and very fast method of bootstrap for sampling without replacement from a finite population is proposed. This method can be used to estimate the variance in sampling with unequal inclusion probabilities and does not require artificial populations or utilization of bootstrap weights. The bootstrap samples are directly selected from the original sample. The bootstrap procedure contains two steps: in the first step, units are selected once with Poisson sampling using the same inclusion probabilities as the original design. In the second step, amongst the non-selected units, half of the units are randomly selected twice. This procedure enables us to efficiently estimate the variance. A set of simulations show the advantages of this new resampling method.
Bootstrap methods for sample selected by two phase sampling design
Variance estimation of inequality indices in complex sampling designs
New bootstraps methods for complex sampling design in finite population
Bootstrap Methods for Two-Phase Sampling With Poisson Design at the Second Phase
In order to provide an unbiased estimator of the variance, the most frequently used sampling design in existing bootstrap methods is simple random sampling with replacement. Nevertheless when these methods do not take the sampling design into account, they provide biased variance estimators. Resampled units usually need to be rescaled or weighted to correct this bias. Another set of methods consists of constructing artificial populations and to resampling from them. These methods are very often time-consuming and have rounding problems. Furthermore, when the sampling design is of several phases, implementation of these bootstrap methods becomes very difficult. We present new sampling methods for two-phase sampling with Poisson design at the second-phase. In this paper, only the cases where the second phase design is Poisson are considered. The reason for this restriction is the connection between this type of two-phase design and lots of missing data problems where the non response is not ignorable. These methods consist of resampling only a subsample of the units in the second phase. This subsample is selected randomly in such a way that it directly reproduces the appropriate variance, without having to rescale or create artificial population. The main advantage of the method is its simplicity, especially for after treatments, such as calibration or imputation for nonresponse. These techniques can be directly applied to bootstrap samples. That is why the proposed method could be particularly worthwhile in real applications.
Simple random sampling with over-replacement
There are several ways to select units with replacement and an equal inclusion expectation. We present a new sampling design called simple random sampling with over-replacement. Its interest lies in the high variance produced for the Horvitz–Thompson estimator. This characteristic could be useful for resampling methods.
Variance estimation via resampling methods for complex sampling designs
A Direct Bootstrap Method for Complex Sampling Designs from a Finite Population
In complex designs, classical bootstrap methods result in a biased variance estimator when the sampling design is not taken into account. Resampled units are usually rescaled or weighted in order to achieve unbiasedness in the linear case. In the present article, we propose novel resampling methods that may be directly applied to variance estimation. These methods consist of selecting subsamples under a completely different sampling scheme from that which generated the original sample, which is composed of several sampling designs. In particular, a portion of the subsampled units is selected without replacement, while another is selected with replacement, thereby adjusting for the finite population setting. We show that these bootstrap estimators directly and precisely reproduce unbiased estimators of the variance in the linear case in a time-efficient manner, and eliminate the need for classical adjustment methods such as rescaling, correction factors, or artificial populations. Moreover, we show via simulation studies that our method is at least as efficient as those currently existing, which call for additional adjustment. This methodology can be applied to classical sampling designs, including simple random sampling with and without replacement, Poisson sampling, and unequal probability sampling with and without replacement.