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

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 thelatter 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-ofthumb 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.