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Article

Some Empirical Results on Nearest-Neighbour Pseudo-populations for Resampling from Spatial Populations

by
Sara Franceschi
1,*,
Rosa Maria Di Biase
2,
Agnese Marcelli
3,4 and
Lorenzo Fattorini
1
1
Department of Economic and Statistics, University of Siena, 53100 Siena, Italy
2
Department of Sociology and Social Research, University of Milano Bicocca, 20126 Milan, Italy
3
Department for Innovation in Biological, Agro-Food and Forest Systems, University of Tuscia, 01100 Viterbo, Italy
4
Department of Sustainable Agro-Ecosystems and Bioresources, Fondazione Edmund Mach, Research and Innovation Centre, 38098 San Michele all’Adige, Italy
*
Author to whom correspondence should be addressed.
Stats 2022, 5(2), 385-400; https://doi.org/10.3390/stats5020022
Submission received: 20 March 2022 / Revised: 11 April 2022 / Accepted: 12 April 2022 / Published: 15 April 2022
(This article belongs to the Special Issue Re-sampling Methods for Statistical Inference of the 2020s)
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Abstract

In finite populations, pseudo-population bootstrap is the sole method preserving the spirit of the original bootstrap performed from iid observations. In spatial sampling, theoretical results about the convergence of bootstrap distributions to the actual distributions of estimators are lacking, owing to the failure of spatially balanced sampling designs to converge to the maximum entropy design. In addition, the issue of creating pseudo-populations able to mimic the characteristics of real populations is challenging in spatial frameworks where spatial trends, relationships, and similarities among neighbouring locations are invariably present. In this paper, we propose the use of the nearest-neighbour interpolation of spatial populations for constructing pseudo-populations that converge to real populations under mild conditions. The effectiveness of these proposals with respect to traditional pseudo-populations is empirically checked by a simulation study.
Keywords: spatial surveys; Horvitz–Thompson estimator; spatially balance sampling; nonmeasurable designs; pseudo-population bootstrap; nearest-neighbour criterion; simulation study spatial surveys; Horvitz–Thompson estimator; spatially balance sampling; nonmeasurable designs; pseudo-population bootstrap; nearest-neighbour criterion; simulation study

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MDPI and ACS Style

Franceschi, S.; Di Biase, R.M.; Marcelli, A.; Fattorini, L. Some Empirical Results on Nearest-Neighbour Pseudo-populations for Resampling from Spatial Populations. Stats 2022, 5, 385-400. https://doi.org/10.3390/stats5020022

AMA Style

Franceschi S, Di Biase RM, Marcelli A, Fattorini L. Some Empirical Results on Nearest-Neighbour Pseudo-populations for Resampling from Spatial Populations. Stats. 2022; 5(2):385-400. https://doi.org/10.3390/stats5020022

Chicago/Turabian Style

Franceschi, Sara, Rosa Maria Di Biase, Agnese Marcelli, and Lorenzo Fattorini. 2022. "Some Empirical Results on Nearest-Neighbour Pseudo-populations for Resampling from Spatial Populations" Stats 5, no. 2: 385-400. https://doi.org/10.3390/stats5020022

APA Style

Franceschi, S., Di Biase, R. M., Marcelli, A., & Fattorini, L. (2022). Some Empirical Results on Nearest-Neighbour Pseudo-populations for Resampling from Spatial Populations. Stats, 5(2), 385-400. https://doi.org/10.3390/stats5020022

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