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There are two distinct types of domains, design- and cross-classes domains, with the former extensively studied under the topic of small-area estimation. In natural resource inventory, however, most classes listed in the condition tables of national inventory programs are characterized as cross-classes domains, such as vegetation type, productivity class, and age class. To date, challenges remain active for inventorying cross-classes domains because these domains are usually of unknown sampling frame and spatial distribution with the result that inference relies on population-level as opposed to domain-level sampling. Multiple challenges are noteworthy: (1) efficient sampling strategies are difficult to develop because of little priori information about the target domain; (2) domain inference relies on a sample designed for the population, so within-domain sample sizes could be too small to support a precise estimation; and (3) increasing sample size for the population does not ensure an increase to the domain, so actual sample size for a target domain remains highly uncertain, particularly for small domains. In this paper, we introduce a design-based generalized systematic adaptive cluster sampling (GSACS) for inventorying cross-classes domains. Design-unbiased Hansen-Hurwitz and Horvitz-Thompson estimators are derived for domain totals and compared within GSACS and with systematic sampling (SYS). Comprehensive Monte Carlo simulations show that (1) GSACS Hansen-Hurwitz and Horvitz-Thompson estimators are unbiased and equally efficient, whereas the latter outperforms the former for supporting a sample of size one; (2) SYS is a special case of GSACS while the latter outperforms the former in terms of increased efficiency and reduced intensity; (3) GSACS Horvitz-Thompson variance estimator is design-unbiased for a single SYS sample; and (4) rules-of-thumb summarized with respect to sampling design and spatial effect improve precision. Because inventorying a mini domain is analogous to inventorying a rare variable, alternative network sampling procedures are also readily available for inventorying cross-classes domains.


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Cross-classes domain inference with network sampling for natural resource inventory

Show Author's information Zhengyang HouaRonald E. McRobertsbChunyu Zhanga( )Göran StåhlcXiuhai ZhaoaXuejun WangdBo LieQing Xuf
The Key Laboratory for Silviculture and Conservation of Ministry of Education, Beijing Forestry University, Beijing, China
Department of Forest Resources, University of Minnesota, Saint Paul, MN, United States
Department of Forest Resource Management, Swedish University of Agricultural Sciences, Umeå, Sweden
Office of the National Forestry and Grassland Administrations Forest Resources Supervision Commissioner in Beijing, Beijing, China
Department of Statistics, University of Illinois at Urbana-Champaign, Champaign, IL, United States
Key Laboratory on the Science and Technology of Bamboo and Rattan, International Centre for Bamboo and Rattan, Beijing, China

Abstract

There are two distinct types of domains, design- and cross-classes domains, with the former extensively studied under the topic of small-area estimation. In natural resource inventory, however, most classes listed in the condition tables of national inventory programs are characterized as cross-classes domains, such as vegetation type, productivity class, and age class. To date, challenges remain active for inventorying cross-classes domains because these domains are usually of unknown sampling frame and spatial distribution with the result that inference relies on population-level as opposed to domain-level sampling. Multiple challenges are noteworthy: (1) efficient sampling strategies are difficult to develop because of little priori information about the target domain; (2) domain inference relies on a sample designed for the population, so within-domain sample sizes could be too small to support a precise estimation; and (3) increasing sample size for the population does not ensure an increase to the domain, so actual sample size for a target domain remains highly uncertain, particularly for small domains. In this paper, we introduce a design-based generalized systematic adaptive cluster sampling (GSACS) for inventorying cross-classes domains. Design-unbiased Hansen-Hurwitz and Horvitz-Thompson estimators are derived for domain totals and compared within GSACS and with systematic sampling (SYS). Comprehensive Monte Carlo simulations show that (1) GSACS Hansen-Hurwitz and Horvitz-Thompson estimators are unbiased and equally efficient, whereas the latter outperforms the former for supporting a sample of size one; (2) SYS is a special case of GSACS while the latter outperforms the former in terms of increased efficiency and reduced intensity; (3) GSACS Horvitz-Thompson variance estimator is design-unbiased for a single SYS sample; and (4) rules-of-thumb summarized with respect to sampling design and spatial effect improve precision. Because inventorying a mini domain is analogous to inventorying a rare variable, alternative network sampling procedures are also readily available for inventorying cross-classes domains.

Keywords: Forest inventory, Design-based inference, Cross-classes domain estimation, Network sampling, Generalized systematic adaptive cluster sampling

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Publication history

Received: 22 January 2022
Revised: 10 March 2022
Accepted: 14 March 2022
Published: 24 March 2022
Issue date: June 2022

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© 2022 The Authors.

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Acknowledgements

This work was supported by (1) the Fundamental Research Funds for the Central Universities (Grant No. 2021ZY04), (2) the National Natural Science Foundation of China (Grant No. 32001252), and (3) the International Center for Bamboo and Rattan (Grant No. 1632020029).

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This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).

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