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Variance estimation in stratified adaptive cluster sampling

100%
Yasmeen U., Noor-ul-Amin M., Hanif M.
Statistics in Transition new series
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2022
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vol. 23
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issue 1
173-184
EN
In many sampling surveys, the use of auxiliary information at either the design or estimation stage, or at both these stages is usual practice. Auxiliary information is commonly used to obtain improved designs and to achieve a high level of precision in the estimation of population density. Adaptive cluster sampling (ACS) was proposed to observe rare units with the purpose of obtaining highly precise estimations of rare and specially clustered populations in terms of least variances of the estimators. This sampling design proved to be more precise than its more conventional counterparts, including simple random sampling (SRS), stratified sampling, etc. In this paper, a generalised estimator is anticipated for a finite population variance with the use of information of an auxiliary variable under stratified adaptive cluster sampling (SACS). The bias and mean square error expressions of the recommended estimators are derived up to the first degree of approximation. A simulation study showed that the proposed estimators have the least estimated mean square error under the SACS technique in comparison to variance estimators in stratified sampling.
2
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A new family of robust regression estimators utilizing robust regression tools and supplementary attributes

88%
Sajjad I., Hanif M., Koyuncu N., Shahzad U., Al-Noor N. H.
Statistics in Transition new series
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2021
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vol. 22
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issue 1
207-216
EN
Zaman and Bulut (2018a) developed a class of estimators for a population mean utilising LMS robust regression and supplementary attributes. In this paper, a family of estimators is proposed, based on the adaptation of the estimators presented by Zaman (2019), followed by the introduction of a new family of regression-type estimators utilising robust regression tools (LAD, H-M, LMS, H-MM, Hampel-M, Tukey-M, LTS) and supplementary attributes. The mean square error expressions of the adapted and proposed families are determined through a general formula. The study demonstrates that the adapted class of the Zaman (2019) estimators is in every case more proficient than that of Zaman and Bulut (2018a). In addition, the proposed robust regression estimators based on robust regression tools and supplementary attributes are more efficient than those of Zaman and Bulut (2018a) and Zaman (2019).The theoretical findings are supported by real-life examples.
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