A unified principled framework for resampling based on pseudo-populations: asymptotic theory. (English) Zbl 1466.62241
Summary: In this paper, a class of resampling techniques for finite populations under \(\pi\) ps sampling design is introduced. The basic idea on which they rest is a two-step procedure consisting in: (i) constructing a “pseudo-population” on the basis of sample data; (ii) drawing a sample from the predicted population according to an appropriate resampling design. From a logical point of view, this approach is essentially based on the plug-in principle by Efron, at the “sampling design level”. Theoretical justifications based on large sample theory are provided. New approaches to construct pseudo populations based on various forms of calibrations are proposed. Finally, a simulation study is performed.
MSC:
| 62D05 | Sampling theory, sample surveys |
| 62G09 | Nonparametric statistical resampling methods |
| 62E20 | Asymptotic distribution theory in statistics |
Keywords:
\(\pi\) ps sampling designs; bootstrap; calibration; confidence intervals; finite populations; resampling; variance estimationReferences:
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