Estimation of general parameters under stratified adaptive cluster sampling based on dual use of auxiliary information

Document Type : Article

Authors

Department of Statistics Quaid-i-Azam University, Islamabad, Pakistan

Abstract

Auxiliary information is mostly used together with study variable to enhance
efficiency of estimators for population mean, total and variance. Thompson
introduced adaptive cluster sampling as an appropriate sampling scheme for
rare and clustered populations. In present article, difference-type and
difference-cum-exponential-ratio-type estimators are presented utilizing two
auxiliary variables for estimation of general parameter under stratified
adaptive cluster sampling. Proposed estimators utilize auxiliary information
in terms of ranks, variances and means of auxiliary variables in $h^{th}$
stratum. Expressions for bias and mean square error of proposed estimators
are derived using first order of approximation. Numerical study is conducted
to evaluate the performance of proposed estimators.

Keywords

Main Subjects

References

References:
[1] Thompson, S. K. “Adaptive cluster sampling”, J. Am. Stat. Assoc., 85(412), pp. 1050-1059 (1990).
[2] Chutiman, N., Chiangpradit M. and Suraphee S. “Ratio estimator in adaptive cluster sampling based on ranked set”, Adv. Appl. Stat., 49(2), pp. 105-116 (2016).
[3] Gattone, S.A., Giordani, P., Battista, T.D. and Fortuna, F. “Adaptive cluster double sampling with post stratification with application to an epiphytic lichen community”, Environ. Ecol. Stat., 25(1), pp. 125-138 (2018).
[4] Yasmeen, U. and Thompson, M. “Variance estimation in adaptive cluster sampling”, Communications in Statistics - Theory and Methods, https://doi.org/10.1080/03610926.2019.1576890 (2019).
[5] Qureshi, M.N., Khalil, S. and Hanif, M. “ Joint influence of exponential ratio and exponential product estimator for the estimation clustered population mean in adaptive cluster sampling”, Adv. Appl. Stat., 53(1), pp. 13-28 (2018).
[6] Ba¸k, T. “An extension of Horvitz–Thompson estimator used in adaptive cluster sampling to continuous universe”, Comm. Statist. Theory Methods, 46(19), pp. 9777-9786 (2017).
[7] Younis, F. and Shabbir, J. “Estimators for Population Mean in Adaptive Cluster Sampling”, Thail. Stat., 15(2), pp. 105-110 (2017).
[8] Younis, F. and Shabbir, J. “A Class of Hartley-Ross-Type Estimators for Population Mean in Adaptive and Stratified Adaptive Cluster Sampling”, Iran. J. Sci. Technol. Trans. Sci., https://doi.org/10.1007/s40995-018-0552-6 (2018).
[9] Younis, F. and Shabbir, J. “Generalized ratio-type and ratio-exponential-type estimators for population mean under modified Horvitz-Thompson estimator in adaptive cluster sampling”, J. Stat. Comput. Simul., 89(8), pp. 1505-1515 (2019).
[10] Younis, F. and Shabbir, J. “Estimation of general parameter in adaptive cluster sampling using two auxiliary variables”, J.Natn.Sci.Foundation Sri Lanka, 47(1), pp. 89-103 (2019).
[11] Javed, M., Irfan, M. and Pang, T. “Hartley-Ross Type Unbiased Estimators of Population Mean Using Two Auxiliary Variables”, Sci. Iran., DOI: 10.24200/SCI.2018.5648.1397 (2018).
[12] Haq, A., Khan, M. and Hussain, Z. “A new estimator of finite population mean based on the dual use of the auxiliary information”, Comm. Statist. Theory Methods, 46, pp. 4425-4436 (2017).
[13] Shabbir, J. “Efficient utilization of two auxiliary variables in stratified double sampling”, Comm. Statist. Theory Methods, 47(1), pp. 92-101 (2017).
[14] Shabbir, J. and Gupta, S. “On generalized exponential chain ratio estimators under stratified twophase random sampling”, Comm. Statist. Theory Methods, 46, pp. 2910-2920 (2017).
[15] Gupta, S. and Shabbir, J. “On the use of transformed auxiliary variables in estimating population mean by using two auxiliary variables”, J. Stat. Plan. Inference, 137(5), pp. 1606-1611 (2007).
[16] Singh, H. P., Upadhyaya, L. N. and Tailor, R. “Ratio-cum-product type exponential estimator”, Statistica, 69(4), pp. 299-310 (2009).
[17] Choudhury, S. and Singh, B. K. “A class of chain ratio–product type estimators with two auxiliary variables under double sampling scheme”, J. Korean Stat. Soc., 41(2), pp. 247-256 (2012).
[18] Hamad, N., Hanif, M. and Haider, N. “A regression type estimator with two auxiliary variables for two-phase sampling”, Open Journal of Statistics, 3, pp. 74-78 (2013).
[19] Chutiman, N. “Adaptive cluster sampling using auxiliary variable”, Journal of Mathematics and Statistics, 9(3), pp. 249-255 (2013).
[20] Yadav, S. K., Misra, S., Mishra, S. S. and Chutiman, N. “Improved ratio estimators of population mean in adaptive cluster sampling”,J. Stat. Appl. Prob. Lett, 3(1), pp. 1-6 (2016).
[21] Qureshi, M.N., Kadilar, C., Noor Ul Amin, M. and Hanif, M. “Rare and clustered population estimation using the adaptive cluster sampling with some robust measures”, J. Stat. Comput. Simul., 88(14), pp. 2761-2774 (2018).
[22] Vishwakarma, G.K. and Gangele, R. K. “A class of chain ratio-type exponential estimators in double sampling using two auxiliary variates”, Appl. Math. Comput., 227, pp.171-175 (2014).
[23] Singh, G.N. and Khalid, M. “Exponential chain dual to ratio and regression type estimators of population mean in two phase sampling”, Statistica, 75(4), pp. 379-389 (2015).
[24] Khan, M. and Al-Hossain, A. Y. “A note on a difference-type estimator for population mean under two-phase sampling design”, SpringerPlus, 5(1):723, DOI: 10.1186/s40064-016-2368-1 (2016).
[25] Khan, M.“A ratio chain-type exponential estimator for finite population mean using double sampling”, SpringerPlus, 5:86, DOI: 10.1186/s40064-016-1717-4 (2016).
[26] Singh, H. P., Pal, S. K. and Solanki, R. S. “A new class of estimators of finite population mean in sample surveys”, Comm. Statist. Theory Methods, 46, pp. 2630-2637 (2017).
[27] Shabbir, J. and Gupta, S. “Estimation of finite population mean in simple and stratified random sampling using two auxiliary variables”, Comm. Statist. Theory Methods, 46(20), pp. 10135-10148 (2017).
[28] Muneer, S., Shabbir, J. and Khalil, A.“Estimation of finite population mean in simple random sampling and stratified random sampling using two auxiliary variables”, Comm. Statist. Theory Methods, 46(5), pp. 2181-2192 (2017).
[29] Singh, R., Chauhan, P., Sawan, N. and Smarandache, F.“Improved exponential estimator for population variance using two auxiliary variables”, Octogon Math. Mag., 17(2), pp. 667-674 (2009).
[30] Singh, H. P. and Solanki, R. S. “A new procedure for variance estimation in simple random sampling using auxiliary information”, Statist. Papers, 54(2), pp. 479-497 (2013).
[31] Olufadi, Y. and Kadilar, C.“A study on the chain ratio-type estimator of finite population variance”, J. probab. stat., pp. 1-5 (2014).
[32] Amin, M.N.U., Yasmeen, U.and Hanif, M.“Generalized variance estimators in adaptive cluster sampling using single auxiliary variable”, J. Stat. Manag. Syst., 21(3), pp. 401-415 (2018).
[33] Smith, D. R., Conroy, M. J. and Brakhage, D. H. “Efficiency of adaptive cluster sampling for estimating density of wintering waterfowl”, Biometrics, 51(2), pp.777-788 (1995).
[34] Dryver A. L. and Chao, C.-T. “Ratio estimators in adaptive cluster sampling”, Environmetrics, 18(6), pp. 607-620 (2007).
[35] Chao, C.-T., Dryver, A. L. and Chiang, T.C. “Leveraging the rao–blackwell theorem to improve ratio estimators in adaptive cluster sampling”, Environ. Ecol. Stat., 18(3), pp. 543-568 (2011).
[36] Zamanzade, E., and Vock, M. “Variance estimation in ranked set sampling using a concomitant variable”. Statist. Probab. Lett., 105, pp.1-5 (2015).
Scientia Iranica
Volume 28, Issue 3 - Serial Number 3
Transactions on Industrial Engineering (E)
May and June 2021
Pages 1780-1801

Files

History

  • Receive Date: 21 December 2018
  • Revise Date: 12 May 2019
  • Accept Date: 02 September 2019

Share

How to cite

Statistics