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2019 Design-based mapping for finite populations of marked points
Lorenzo Fattorini, Marzia Marcheselli, Caterina Pisani, Luca Pratelli
Electron. J. Statist. 13(1): 2121-2149 (2019). DOI: 10.1214/19-EJS1572

Abstract

The estimation of marks for a finite population of points scattered onto a study region is considered when a sample of these points is selected by a probabilistic sampling scheme. At each point, the mark is estimated by means of an inverse distance weighting interpolator. The design-based asymptotic properties of the resulting maps are derived when the study area remains fixed, a sequence of nested populations with increasing size is considered and samples of increasing size are selected. Conditions ensuring design-based asymptotic unbiasedness and consistency are given. They essentially require that marks are the values of a pointwise or uniformly continuous deterministic function, the enlargement of the populations is rather regular and the sequence of sampling designs ensures an asymptotic spatial balance. A computationally simple mean squared error estimator is proposed. A simulation study is performed to assess the theoretical results on artificial populations. Finally, an application for mapping the values of the height of trees in a forest stand located in North Italy is reported.

Citation

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Lorenzo Fattorini. Marzia Marcheselli. Caterina Pisani. Luca Pratelli. "Design-based mapping for finite populations of marked points." Electron. J. Statist. 13 (1) 2121 - 2149, 2019. https://doi.org/10.1214/19-EJS1572

Information

Received: 1 June 2018; Published: 2019
First available in Project Euclid: 28 June 2019

zbMATH: 07080070
MathSciNet: MR3980956
Digital Object Identifier: 10.1214/19-EJS1572

Subjects:
Primary: 62G05
Secondary: 62G20

JOURNAL ARTICLE
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Vol.13 • No. 1 • 2019
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