Trade-off between efficiency and variance estimation of spatially balanced augmented samples
In this paper, we construct three types of augmented samples, which are samples generated from two separate randomization events. The first type combines a simple random sample ( SRS ) with a spatially balanced sample ( SBS ) selected from the same finite population. The second type combines an SBS...
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Veröffentlicht in: | Environmental and ecological statistics 2023-12, Vol.30 (4), p.741-767 |
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Sprache: | eng |
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Zusammenfassung: | In this paper, we construct three types of augmented samples, which are samples generated from two separate randomization events. The first type combines a simple random sample (
SRS
) with a spatially balanced sample (
SBS
) selected from the same finite population. The second type combines an
SBS
with an
SRS
. The third type combines two spatially balanced samples. The simple random sample is constructed without replacement and does not contain any ties. The spatially balanced samples are constructed using the properties of the Halton sequence. We provide the first and second order inclusion probabilities for the augmented samples. Next, using the inclusion probabilities of the augmented samples, we construct estimators for the mean and total of a finite population. The efficiency of the augmented samples varies between the efficiency of
SRS
and
SBS
samples. If the number of
SRS
observations in the augmented sample is large, the efficiency is closer to the efficiency of
SRS
. Otherwise, it is closer to the efficiency of
SBS
. We also provide estimators for the variances of the estimators of population total of augmented samples. The stability of these variance estimators depends on the proportion of
SRS
observations in the augmented samples. The larger number of
SRS
observations lead to stable variance estimators. |
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ISSN: | 1352-8505 1573-3009 |
DOI: | 10.1007/s10651-023-00582-7 |