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adaptive cluster sampling with a data driven stopping rule

STATISTICAL METHODS AND APPLICATIONS 2011年第1期20卷 1-21页

作者： Gattone, Stefano A. Di Battista, Tonio Univ Roma Tor Vergata Dept SEFeMeQ Rome Italy Univ G DAnnunzio Dept DMQTE Chieti Italy

The adaptive cluster sampling (ACS) is a suitable sampling design for rare and clustered populations. In environmental and ecological applications, biological populations are generally animals or plants with highly patchy spatial distribution. However, ACS would be a less efficient design when the study population is not rare with low aggregation since the final sample size could be easily out of control. In this paper, a new variant of ACS is proposed in order to improve the performance (in term of precision and cost) of ACS versus simple random sampling (SRS). The idea is to detect the optimal sample size by means of a data-driven stopping rule in order to determine when to stop the adaptive procedure. By introducing a stopping rule the theoretical basis of ACS are not respected and the behaviour of the ordinary estimators used in ACS is explored by using Monte Carlo simulations. Results show that the proposed variant of ACS allows to control the effective sample size and to prevent from excessive efficiency loss typical of ACS when the population is less clustered than anticipated. The proposed strategy may be recommended especially when no prior information about the population structure is available as it does not require a prior knowledge of the degree of rarity and clustering of the population of interest.

关键词： adaptive cluster sampling Monte carlo simulation Stopping rule Efficiency

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adaptive cluster sampling with networks selected without replacement

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BIOMETRIKA 1997年第1期84卷 209-219页

作者： Salehi, M Seber, GAF Statistics Department Auckland University Auckland Private Bag 92019 New Zealand

In the adaptive cluster design introduced by Thompson (1990), a finite population of units under investigation is partitioned into networks on the basis of a specified condition for adding neighbourhoods to a sampled unit. An initial sample of units is taken and a network may be sampled more than once. In this paper, we introduce a-modification of the design in which networks are sampled only once. Two unbiased estimators are considered and the Rao-Blackwell theorem is used to improve them in terms of efficiency. The various estimators are compared using two examples.

关键词： adaptive cluster sampling Murthy's unordered estimator networks without replacement Raj estimator Rao-Blackwell method

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adaptive cluster sampling for estimation of abundances within local populations of low-abundance plants

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ECOLOGY 2005年第5期86卷 1091-1100页

作者： Philippi, T Florida Int Univ Dept Biol Sci Miami FL 33199 USA Florida Int Univ Coastal Everglades LTER Miami FL 33199 USA

Quantitative estimates of abundance for rare plants can be difficult, as the most widely used sampling techniques are ill-suited for rarity. adaptive cluster sampling (ACS) can take advantage of the spatial clustering common in rare plant populations to provide more efficient unbiased estimates of population sizes than simple random sampling. When plants are found in a quadrat, all adjacent quadrats are adaptively added to the sample. Despite this biased sampling, the Horvitz-Thompson estimator for adaptive cluster sampling provides unbiased estimates of population means or totals, and variances of those estimates. Because ACS disproportionately samples quadrats with plants, it can provide additional efficiency whenever further attributes of rare individuals need to be assessed, such as demographic parameters or genotypes. adaptive cluster sampling was performed on a population of Aletris bracteata, a moderately visible herbaceous species, in a savanna near Chekika, Everglades National Park, Florida. Both 1-m(2) and 4-m(2) quadrats provided reasonable estimates of the population size. The 1-m(2) sampling included 30-36% of the estimated total plants while sampling only 5% of the total area. The 4-m(2) sampling captured 78% of the estimated total population while sampling only 21% of the area.

关键词： adaptive cluster sampling Aletris bracteata Chekika population abundance rare plant sampling

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adaptive cluster sampling with clusters selected without replacement and stopping rule

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ENVIRONMENTAL AND ECOLOGICAL STATISTICS 2016年第3期23卷 453-468页

作者： Gattone, Stefano Antonio Mohamed, Esha Di Battista, Tonio Univ G dAnnunzio DiSFPEQ Chieti Italy Univ Trier Dept Social Stat Trier Germany

adaptive cluster sampling (ACS) has received much attention in recent years since it yields more precise estimates than conventional sampling designs when applied to rare and clustered populations. These results, however, are impacted by the availability of some prior knowledge about the spatial distribution and the absolute abundance of the population under study. This prior information helps the researcher to select a suitable critical value that triggers the adaptive search, the neighborhood definition and the initial sample size. A bad setting of the ACS design would worsen the performance of the adaptive estimators. In particular, one of the greatest weaknesses in ACS is the inability to control the final sampling effort if, for example, the critical value is set too low. To overcome this drawback one can introduce ACS with clusters selected without replacement where one can fix in advance the number of distinct clusters to be selected or ACS with a stopping rule which stops the adaptive sampling when a predetermined sample size limit is reached or when a given stopping rule is verified. However, the stopping rule breaks down the theoretical basis for the unbiasedness of the ACS estimators introducing an unknown amount of bias in the estimates. The current study improves the performance of ACS when applied to patchy and clustered but not rare populations and/or less clustered populations. This is done by combining the stopping rule with ACS without replacement of clusters so as to further limit the sampling effort in form of traveling expenses by avoiding repeat observations and by reducing the final sample size. The performance of the proposed design is investigated using simulated and real data.

关键词： adaptive cluster sampling Raj estimator Stopping rule

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On estimating the finite population mean using improved estimators in adaptive cluster sampling design

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Journal of Radiation Research and Applied Sciences 2025年第3期18卷

作者： Rohan Mishra Diaa S. Metwally Rajesh Singh Nitesh Kumar Adichwal School of Management IILM University Knowledge Park II Greater Noida 201306 Uttar Pradesh India Department of Accounting Faculty of Business Imam Mohammad Ibn Saud Islamic University (IMSIU) Riyadh 11432 Saudi Arabia Department of Statistics Institute of Science Banaras Hindu University Varanasi 221005 Uttar Pradesh India

This article introduces a generalized class of estimators tailored for estimating the finite population mean within the framework of adaptive cluster sampling (ACS) design. The proposed class is designed to encompass numerous existing estimators as its particular cases while also introducing several new novel estimators. It should be noted that the existing estimators which are presented in Section 3 are members of the proposed log type generalized class T g . From the proposed log type generalized class T g , four new log type estimators are developed. We derive the expressions for bias and mean square error (MSE) up to the first order of approximation. Through simulation studies and a real data application, we compare the performance of the new estimators derived from this proposed class with existing ones, demonstrating that the newly developed estimators outperform their existing counterparts. For the better understanding of the performances of our suggested class of estimators, we present the numerical results graphically.

关键词： Log type estimator adaptive cluster sampling Optimizing scalars Simulation Rare events Hidden clustered Thorny plants Mathematics Subject Classification: 62D05 62P12

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Adjusted two-stage adaptive cluster sampling

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APPLIED MATHEMATICS AND COMPUTATION 2002年第1期126卷 83-95页

作者： Khan, A Muttlak, HA Univ Dhaka ISRT Dhaka 1000 Bangladesh Deakin Univ Sch Comp & Math Geelong Vic 3217 Australia

An adjusted two-stage sampling procedure is discussed for adaptive cluster sampling where some network,,, are large and others are small. A two-stage sample is drawn from the large networks and a single-stage sample is drawn from the rest. The simple random sampling (SRS) procedure is used at the second stage. An estimator for the population mean along with its properties is discussed. (C) 2002 Elsevier Science Inc. All rights reserved.

关键词： adaptive cluster sampling network simple random sampling two-stage sampling

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Searching for rare species: A comparison of Floristic Habitat sampling and adaptive cluster sampling for detecting and estimating abundance

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FOREST ECOLOGY AND MANAGEMENT 2018年 407卷 1-8页

作者： Bowering, Rebecca Wigle, Rachel Padget, Tegan Adams, Blair Cote, Dave Wiersma, Yolanda F. Mem Univ Dept Biol St John NF A1B 3X9 Canada Dept Fisheries & Land Resources Forestry & Wildlife Res Forestry & Wildlife Branch Corner Brook NF A1V 2T6 Canada Fisheries & Oceans Canada 80 East White Hills Rd St John NF A1C 5X1 Canada

Surveys of rare species are challenging owing to the difficulty of detecting them on a landscape. Survey methods vary, often to achieve different goals. Thus when different survey methods are used in different locations and/or years, it is difficult to compare abundance data between regions or for assessing population trends through time. In many jurisdictions, forest legislation or policy may require managers to carry out surveys to assess presence or confirm absence of rare species. This then can inform forest management decisions that may impact these species, particularly when the rare species is listed for protection, for example under species-at-risk legislation. Because species surveys can be time consuming as managers want to be confident in their ability to detect species (or confirm that observed absences are likely true), survey protocols should be as efficient and effective as possible. Floristic habitat sampling (FHS) is often applied for botanical surveys and focuses on generating a list of species present in a region (sometimes referred to as the releve method) by inventorying an area as thoroughly as possible, including potential microhabitats. The adaptive cluster sampling (ACS) method assumes that rare species are clustered in space and delineates sample plots non-randomly to increase accuracy of abundance estimates. Here, we compare FHS and ACS methods to detect rare lichens in two landscapes on the Avalon Peninsula in Newfoundland, as well as to generate species lists of arboreal lichens in a region. We also carry out a novel field simulation using artificial lichens to test how well ACS estimates known abundance. Finally, we demonstrate the utility of ACS to make new detections of an IUCN red-listed species (Erioderma pedicellatum) in a real-world setting and suggest how survey methods can be chosen to meet different forest management requirements.

关键词： Rare species sampling Lichens Erioderma pedicellatum Floristic sampling adaptive cluster sampling

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Analytical expressions for Rao-Blackwell estimators in adaptive cluster sampling

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JOURNAL OF STATISTICAL PLANNING AND INFERENCE 2000年第1-2期84卷 221-236页

作者： Félix-Medina, MH Penn State Univ Dept Stat University Pk PA 16802 USA Univ Autonoma Sinaloa Esc Ciencias Fis Matemat Culiacan Mexico

In this paper, we consider adaptive cluster sampling with the initial sample selected either by simple random sampling without replacement or by unequal probability sampling with replacement. We derive analytical expressions for the Rao-Blackwell versions of the following two estimators originally proposed by Thompson (1990, J. Amer. Statist. Assoc. 85, 1050-1059): the modified Horvitz-Thompson estimator and the modified Hansen-Hurwitz one. Furthermore, we derive analytical expressions for the variances of the two Rao-Blackwell estimators above mentioned, as well as analytical expressions for unbiased Rao-Blackwell estimators of those variances. In the without-replacement case, the derivations are based on the multivariate hypergeometric distribution, whereas in the with-replacement case, they are based on the multinomial distribution. (C) 2000 Elsevier Science B.V. All rights reserved.

关键词： adaptive cluster sampling design-based inferential approach finite population minimal sufficient statistic Rao-Blackwell theorem simple random sampling unequal probability sampling

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Leveraging the Rao-Blackwell theorem to improve ratio estimators in adaptive cluster sampling

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ENVIRONMENTAL AND ECOLOGICAL STATISTICS 2011年第3期18卷 543-568页

作者： Chao, Chang-Tai Dryver, Arthur L. Chiang, Tzu-Ching Natl Cheng Kung Univ Dept Stat Sch Management Tainan 70101 Taiwan Natl Inst Dev Adm Grad Sch Business Adm Bangkok 10240 Thailand

Rao-Blackwellization is used to improve the unbiased Hansen-Hurwitz and Horvitz-Thompson unbiased estimators in adaptive cluster sampling by finding the conditional expected value of the original unbiased estimators given the sufficient or minimal sufficient statistic. In principle, the same idea can be used to find better ratio estimators, however, the calculation of taking all the possible combinations into account can be extremely tedious in practice. The simplified analytical forms of such ratio estimators are not currently available. For practical interest, several improved ratio estimators in adaptive cluster sampling are proposed in this article. The proposed ratio estimators are not the real Rao-Blackwellized versions of the original ones but make use of the Rao-Blackwellized univariate estimators. How to calculate the proposed estimators is illustrated, and their performance are evaluated by both of the Bivariate Poisson clustered process and a real data. The simulation result indicates that the proposed improved ratio estimators are able to provide considerably advantageous estimation results over the original ones.

关键词： adaptive cluster sampling Ratio estimator Rao-Blackwellization Sufficient statistic Minimal sufficient statistic Hansen-Hurwitz estimation Horvitz-Thompson estimation

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The use of adaptive cluster sampling for hydroacoustic surveys

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ICES JOURNAL OF MARINE SCIENCE 2002年第6期59卷 1314-1325页

作者： Conners, ME Schwager, SJ Cornell Univ Dept Biometr Ithaca NY 14853 USA

Resource managers are often required to estimate the size of a wildlife population based on sampling surveys. This problem is especially critical in fisheries, where stock-size estimation forms the basis for key policy decisions. This study looks at design-based methods for a hydroacoustic fisheries survey, with the goal of improving estimation when the target stock has a patchy spatial distribution. In particular, we examine the efficiency and feasibility of a relatively new design-based method known as adaptive cluster sampling (ACS). A simulation experiment looks at the relative efficiency of ACS and traditional sampling designs in a hydroacoustic survey setting. Fish densities with known spatial covariance are generated and subjected to repeated sampling. The distributions of the different estimators are compared. Hydroacoustic data frequently display strong serial correlation along transects and so traditional designs based on one-stage cluster sampling are appropriate. Estimates of total stock size for these designs had a markedly skewed distribution. ACS designs performed better than traditional designs for all stocks with small-scale spatial correlation in fish density, yielding estimates with lower variance. ACS estimators were not skewed and had a lower frequency of large errors. For the most variable stock the use of ACS reduced the coefficient of variation (CV) of the stock size estimate from over 0.9 to around 0.5. Differences between traditional and ACS designs were consistent over multiple realizations of each spatial covariance model. A survey of rainbow smelt (Osmerus mordax) in the eastern basin of Lake Erie was used as a case study for development of a survey design. A field trial showed that use of ACS for the survey is feasible but pointed out some areas for further research. The biggest drawback to use of ACS is uncertainty in the final sample size. This can be partially controlled by applying ACS within a stratified design. ACS retains the unb

关键词： adaptive cluster sampling survey design spatial sampling stock assessment patchy distributions

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