{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,10]],"date-time":"2026-02-10T20:40:57Z","timestamp":1770756057132,"version":"3.50.0"},"reference-count":24,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2025,3,1]],"date-time":"2025-03-01T00:00:00Z","timestamp":1740787200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Mahasarakham University","award":["6801007"],"award-info":[{"award-number":["6801007"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Adaptive cluster sampling (ACS) is an efficient sampling technique for studying populations where the characteristic of interest is rare or spatially clustered. This method is widely applied in fields such as ecological studies, epidemiology, and resource management. ACS initially selects sampling units using simple random sampling without replacement. However, in some cases, selected networks may overlap, leading to multiple networks being included in the sample. To address this issue, a modified version of ACS was developed to ensure sampling without replacement at the network level, maintaining sampling symmetry and preventing the inclusion of overlapping networks. Despite this adjustment, asymmetry may still occur when network formation is highly irregular. This issue can be mitigated by incorporating auxiliary variables, which help correct distortions in the sampling process. In many situations, auxiliary variables related to the variable of interest can be utilized to enhance the precision of population parameter estimates. This research proposes multiplicative generalization for an estimator with two auxiliary variables using adaptive cluster sampling with networks selected without replacement. The bias and mean square error (MSE) are derived using a Taylor series expansion to determine the optimal conditions for minimizing MSE. A simulation study is conducted to support the theoretical findings. The results show that the proposed estimator under the optimal values of T1 and T2 is the most efficient to minimize MSE.<\/jats:p>","DOI":"10.3390\/sym17030375","type":"journal-article","created":{"date-parts":[[2025,3,3]],"date-time":"2025-03-03T09:04:49Z","timestamp":1740992689000},"page":"375","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Improved Estimator Using Auxiliary Information in Adaptive Cluster Sampling with Networks Selected Without Replacement"],"prefix":"10.3390","volume":"17","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-6705-3295","authenticated-orcid":false,"given":"Nipaporn","family":"Chutiman","sequence":"first","affiliation":[{"name":"Department of Mathematics, Faculty of Science, Mahasarakham University, Maha Sarakham 44150, Thailand"}]},{"ORCID":"https:\/\/orcid.org\/0009-0008-3161-719X","authenticated-orcid":false,"given":"Athipakon","family":"Nathomthong","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Science, Mahasarakham University, Maha Sarakham 44150, Thailand"}]},{"ORCID":"https:\/\/orcid.org\/0009-0003-6491-3407","authenticated-orcid":false,"given":"Supawadee","family":"Wichitchan","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Science, Mahasarakham University, Maha Sarakham 44150, Thailand"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9027-431X","authenticated-orcid":false,"given":"Pannarat","family":"Guayjarernpanishk","sequence":"additional","affiliation":[{"name":"Faculty of Interdisciplinary Studies, Nong Khai Campus, Khon Kaen University, Nong Khai 43000, Thailand"}]}],"member":"1968","published-online":{"date-parts":[[2025,3,1]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1050","DOI":"10.1080\/01621459.1990.10474975","article-title":"Adaptive cluster sampling","volume":"85","author":"Thompson","year":"1990","journal-title":"J. Am. Statist. Assoc."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"207","DOI":"10.1007\/s10342-005-0074-6","article-title":"Adaptive cluster sampling for estimation of deforestation rates","volume":"124","author":"Magnussen","year":"2005","journal-title":"Eur. J. For. Res."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"59","DOI":"10.2193\/0091-7648(2006)34[59:EOACAR]2.0.CO;2","article-title":"Efficiency of adaptive cluster and random sampling in detecting terrestrial herpetofauna in a tropical rainforest","volume":"34","author":"Noon","year":"2006","journal-title":"Wildl. Soc. Bull."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"86","DOI":"10.3394\/0380-1330(2008)34[86:ACSEDO]2.0.CO;2","article-title":"Adaptive cluster sampling: Estimating density of spatially autocorrelated larvae of the sea lamprey with improved precision","volume":"34","author":"Sullivan","year":"2008","journal-title":"J. Great Lakes Res."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"7","DOI":"10.1023\/A:1021956617984","article-title":"Application of adaptive cluster sampling to low-density populations of freshwater mussels","volume":"10","author":"Smith","year":"2003","journal-title":"Environ. Ecol. Stat."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"1314","DOI":"10.1006\/jmsc.2002.1306","article-title":"The use of adaptive cluster sampling for hydroacoustic surveys","volume":"59","author":"Conners","year":"2002","journal-title":"ICES J. Mar. Sci."},{"key":"ref_7","first-page":"103","article-title":"Adaptive cluster sampling with model based approach for estimating total number of Hidden COVID-19 carriers in Nigeria","volume":"36","author":"Olayiwola","year":"2020","journal-title":"Stat. J. IAOS"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"1204","DOI":"10.18520\/cs\/v120\/i7\/1202-1210","article-title":"Adaptive cluster sampling-based design for estimating COVID-19 cases with random samples","volume":"120","author":"Chandra","year":"2021","journal-title":"Curr. Sci."},{"key":"ref_9","first-page":"474","article-title":"REDACS: Regional emergency-driven adaptive cluster sampling for effective COVID-19 management","volume":"41","author":"Dinamarca","year":"2022","journal-title":"Stoch. Anal. Appl."},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Hwang, J., Bose, N., and Fan, S. (2019). AUV adaptive sampling methods: A Review. Appl. Sci., 9.","DOI":"10.3390\/app9153145"},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Giouroukis, D., Dadiani, A., Traub, J., Zeuch, S., and Markl, V. (2020, January 13\u201317). A survey of adaptive sampling and filtering algorithms for the internet of things. Proceedings of the 14th ACM International Conference on Distributed and Event Based Systems, Montreal, QC, Canada.","DOI":"10.1145\/3401025.3403777"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"209","DOI":"10.1093\/biomet\/84.1.209","article-title":"Adaptive cluster sampling with networks selected without replacement","volume":"84","author":"Salehi","year":"1977","journal-title":"Biometrika"},{"key":"ref_13","first-page":"307","article-title":"Ratio estimation on adaptive cluster sampling","volume":"42","author":"Chao","year":"2004","journal-title":"J. Chin. Stat. Assoc."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"607","DOI":"10.1002\/env.838","article-title":"Ratio estimators in adaptive cluster sampling","volume":"18","author":"Dryver","year":"2007","journal-title":"Environmetric"},{"key":"ref_15","first-page":"241","article-title":"Ratio estimator using two auxiliary variables for adaptive cluster sampling","volume":"6","author":"Chutiman","year":"2008","journal-title":"Thail. Stat."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"249","DOI":"10.3844\/jmssp.2013.249.255","article-title":"Adaptive cluster sampling using auxiliary variable","volume":"9","author":"Chutiman","year":"2013","journal-title":"J. Math. Stat."},{"key":"ref_17","first-page":"9","article-title":"Efficient estimator for population variance using auxiliary variable","volume":"6","author":"Yadav","year":"2016","journal-title":"Am. J. Oper. Res."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"553","DOI":"10.18187\/pjsor.v11i4.1009","article-title":"Generalized exponential-cum-exponential estimator in adaptive cluster sampling","volume":"11","author":"Chaudhry","year":"2015","journal-title":"Pak. J. Stat. Oper. Res."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"63","DOI":"10.18576\/jsapl\/090201","article-title":"Transformed ratio type estimators under adaptive cluster sampling an application to covid-19","volume":"9","author":"Singh","year":"2022","journal-title":"J. Stat. Appl. Probab. Lett."},{"key":"ref_20","first-page":"46","article-title":"Generalized ratio type estimator under adaptive cluster sampling","volume":"67","author":"Bhat","year":"2022","journal-title":"J. Sci. Res."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"412","DOI":"10.28951\/bjb.v42i4.725","article-title":"On combining ratio and product type estimators for estimation of finite population mean in adaptive cluster sampling design","volume":"42","author":"Mishra","year":"2024","journal-title":"Braz. J. Biom."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"726398","DOI":"10.1155\/2014\/726398","article-title":"Ratio estimator in adaptive cluster sampling without replacement of networks","volume":"2014","author":"Chutiman","year":"2014","journal-title":"J. Probab. Stat."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"269","DOI":"10.1080\/01621459.1956.10501326","article-title":"Some Estimators in sampling with varying probabilities without replacement","volume":"51","author":"Raj","year":"1956","journal-title":"J. Am. Stat. Assoc."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"1606","DOI":"10.1016\/j.jspi.2006.09.008","article-title":"On the use of transformed auxiliary variables in estimating population mean by using two auxiliary variables","volume":"137","author":"Gupta","year":"2007","journal-title":"J. Stat. Plan. 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