Novel Log Type Class Of Estimators Under Ranked Set Sampling
This paper suggests some novel class of log type estimators for the estimation of population mean of study variable under ranked set sampling by utilizing information on population mean of auxiliary variable. The mean square error of the proposed class of estimators is obtained to the first order of...
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| Published in | Sankhyā. Series B (2008) Vol. 84; no. 1; pp. 421 - 447 |
|---|---|
| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
New Delhi
Springer India
01.05.2022
|
| Subjects | |
| Online Access | Get full text |
| ISSN | 0976-8386 0976-8394 |
| DOI | 10.1007/s13571-021-00265-y |
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| Abstract | This paper suggests some novel class of log type estimators for the estimation of population mean of study variable under ranked set sampling by utilizing information on population mean of auxiliary variable. The mean square error of the proposed class of estimators is obtained to the first order of approximation. We have compared the proposed class of estimators with some existing competitors under some specific conditions. The theoretical results are validated by a computational study using real and simulated data sets. On the lines of McIntyre (
Aust. J. Agr. Res.
3
, 385–390
1952
), Dell (
1969
) and Dell and Clutter (
Biometrics
28
, 545–555
1972
), the effect of skewness and kurtosis over the efficiency of the proposed class of estimators have also studied and reported. |
|---|---|
| AbstractList | This paper suggests some novel class of log type estimators for the estimation of population mean of study variable under ranked set sampling by utilizing information on population mean of auxiliary variable. The mean square error of the proposed class of estimators is obtained to the first order of approximation. We have compared the proposed class of estimators with some existing competitors under some specific conditions. The theoretical results are validated by a computational study using real and simulated data sets. On the lines of McIntyre (
Aust. J. Agr. Res.
3
, 385–390
1952
), Dell (
1969
) and Dell and Clutter (
Biometrics
28
, 545–555
1972
), the effect of skewness and kurtosis over the efficiency of the proposed class of estimators have also studied and reported. |
| Author | Kumar, Anoop Bhushan, Shashi |
| Author_xml | – sequence: 1 givenname: Shashi surname: Bhushan fullname: Bhushan, Shashi organization: Department of Mathematics & Statistics, Dr. Shakuntala Misra National Rehabilitation University – sequence: 2 givenname: Anoop orcidid: 0000-0003-2775-6548 surname: Kumar fullname: Kumar, Anoop email: anoop.asy@gmail.com organization: Department of Mathematics & Statistics, Dr. Shakuntala Misra National Rehabilitation University |
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| Cites_doi | 10.1080/00949655.2012.733395 10.1080/08898480.2020.1816703 10.1002/bimj.200390007 10.1007/BF02911622 10.1080/02331888.2018.1477157 10.1080/03610929008830198 10.1080/03610918.2020.1740266 10.1080/03610918.2018.1458133 10.1111/j.1467-9574.1985.tb01149.x 10.1007/978-94-007-0789-4 10.1177/0962280218823793 10.1080/03610926.2020.1725828 10.1080/02664763.2017.1279596 10.1002/bimj.4710340307 10.1080/03610928908829905 10.24200/SCI.2020.54423.3744 10.1080/09720510.1661604 10.1007/s00362-007-0079-y 10.1016/j.spl.2017.05.001 10.1002/bimj.4710380616 10.2174/9789811490491120010007 10.1071/AR9520385 10.2307/2533564 10.1111/1467-9884.00341 10.1016/j.jspi.2008.11.009 10.1007/PL00020899 10.1080/03610926.2020.1777431 10.2307/2556166 10.1080/03610926.2019.1645857 10.1007/s41872-019-00079-y 10.1002/(SICI)1521-4036(199909)41:5<627::AID-BIMJ627>3.0.CO;2-W 10.1080/03610926.2013.830748 10.1002/bimj.4710370704 |
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| Keywords | efficiency Skewness 62D99 mean square error Kurtosis Ranked set sampling 62D05 |
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| References | MuttlakHAParameter estimation in simple linear regression using ranked set samplingBiom. J.19953779981010.1002/bimj.4710370704 MehtaNMandowaraVLA modified ratio-cum-product estimator of finite population mean using ranked set samplingCommun. Stat. Theory Methods201645267276344791310.1080/03610926.2013.830748 KadilarCUnyaziciYCingiHRatio estimator for the population mean using ranked set samplingStat. Pap.200950301309247618910.1007/s00362-007-0079-y Evans, M.J. (1967). Application of ranked set sampling to regeneration surveys in areas direct seeded to long-leaf pine. Master of Forestry Dissertation Louisiana State University, Baton Rouge, LA. Bhushan, S. and Kumar, A (2020a). On optimal classes of estimators under ranked set sampling. Commun. Stat. Theory Methods. https://doi.org/10.1080/03610926.2020.1777431. Shahzad, U., Al-Noor, N.H., Hanif, M., Sajjad, I. and Anas, M.M. (2020b), Imputation based mean estimators in case of missing data utilizing robust regression and variance-covariance matrices. Commun. Stat. Simul. Comput.https://doi.org/10.1080/03610918.2020.1740266. Singh, H.P. and Kakran, M.S. (1993). A modified ratio estimator using known coefficient of kurtosis of an auxiliary character. In: Advanced sampling theory with applications (S. Singh, H.P. Singh, and M.S. Kakran, eds), vol. 2. Kluwer Academic Publishers, Kluwer. SarndalCESwenssonBWretmanJModel assisted survey sampling2003New YorkSpringer1027.62004 BhushanSGuptaRPandeySKSome log-type classes of estimators using auxiliary informationInt. J. Agric. Stat. Sci.201511487491 KoyuncuNKadilarCRatio and product estimator in stratified random samplingJ. Stat. Plan. Infer.200913925522558252364710.1016/j.jspi.2008.11.009 McIntyreGAA method of unbiased selective sampling using ranked setAust. J. Agr. Res.1952338539010.1071/AR9520385 DellTRClutterJLRanked set sampling theory with order statistics backgroundBiometrics19722854555510.2307/2556166 Dell, T.R. (1969). The theory and some applications of ranked set sampling (Doctoral dissertation) University of Georgia, Athens, GA. Shahzad, U., Al-Noor, N.H., Hanif, M. and Sajjad, I. (2020a). An exponential family of median based estimators for mean estimation with simple random sampling scheme. Commun. Stat. Theory Methods. https://doi.org/10.1080/03610926.2020.1725828. BhushanSKumarALog type estimators of population mean under ranked set samplingPredictive Analytics Stat. Big Data Concepts Model.202028477410.2174/9789811490491120010007http://dx.doi.org/10.2174/9789811490491120010007 MuttlakHAMcDonaldLLRanked set sampling and line intercept method: A more efficient procedureBiom. J.19923432934610.1002/bimj.4710340307 UpadhyayaLNSinghHPUse of transformed auxiliary variable in estimating the finite population meanBiom. J.199941627636172023210.1002/(SICI)1521-4036(199909)41:5<627::AID-BIMJ627>3.0.CO;2-W SinghHPEspejoMROn linear regression and ratio estimator using coefficient of variation of auxiliary variateStatistician20035259671973882 ZamanzadeEMahdizadehMUsing ranked set sampling with extreme ranks in estimating the population proportionStat. Methods Med. Res.202029165177405512910.1177/0962280218823793 Ali, N., Ahmad, I., Hanif, M and Shahzad, U (2019). Robust-regression-type estimators for improving mean estimation of sensitive variables by using auxiliary information. Commun. Stat. Theory Methods. https://doi.org/10.1080/03610926.2019.1645857. KhoshnevisanMSinghRChauhanPSawanNSmarandacheFA general family of estimators for estimating population mean using known value of some population parameter(s)Far East J. Theor. Stat.20072218119123567731133.62005 Shahzad, U., Ahmad, I., Oral, E., Hanif, M. and Almanjahie, I. (2020c). Estimation of the population mean by successive use of an auxiliary variable in median ranked set sampling. Math. Popul. Stud.https://doi.org/10.1080/08898480.2020.1816703. Bhushan, S. and Gupta, R. (2019b). An improved log-type family of estimators using attribute. J. Stat. Manag. Syst.https://doi.org/10.1080/09720510.1661604. KadilarCCingiHRatio estimators in stratified random samplingBiom. J200345218225196594610.1002/bimj.200390007 Shahzad, U., Hanif, M., Sajjad, I. and Anas, M.M. (2020d). Quantile regression-ratio-type estimators for mean estimation under complete and partial auxiliary information. Sci. Iran.https://doi.org/10.24200/SCI.2020.54423.3744. HallsLSDellTRTrial of ranked set sampling for forage yieldsFor. Sci.1966122226 SinghSAdvanced sampling theory with applications: How Michael selected Amy, 1&22003The NetherlandsKluwer10.1007/978-94-007-0789-4 PrasadBSome improved ratio type estimators of population mean and ratio in finite population sample surveysCommun. Stat. Theory Methods19891837939298591310.1080/03610928908829905 BhushanSGuptaRSome log-type classes of estimators using auxiliary attributeAdv. Comput. Sci. Technol20191299108 MahdizadehMZamanzadeEKernel-based estimation of P(X > Y ) in ranked set samplingSORT-Stat. Oper. Res. Trans.2016124326635924891356.62063 YuPLHLamKRegression estimator in ranked set samplingBiometrics1997531070108010.2307/2533564 SisodiaBVSDwivediVKA modified ratio estimator using coefficient of variation of auxiliary variableJ. Indian Soc. Agric. Stat.1981331318 UpadhyayaLNSinghHPVosJWEOn the estimations of population means and ratios using supplementary informationStat. Neerlandica19853930931882597410.1111/j.1467-9574.1985.tb01149.x TakahasiKWakimotoKOn unbiased estimates of the population mean based on the sample stratified by means of orderingAnn. Inst. Stat. Math.19682013110.1007/BF02911622 SamawiHMMuttlakHAEstimation of ratio using ranked set samplingBiom. J19963875376410.1002/bimj.4710380616 SinghHPHornSAn alternative estimator for multi-character surveysMetrika1998489910716665981093.62509 SinghHPTailorRSinghSGeneral procedure for estimating the population mean using ranked set samplingJ. Stat. Comput. Simul.201484931945316937110.1080/00949655.2012.733395 MuttlakHAMcDonaldLLRanked set sampling with respect to a concomitant variables and with size biased probability of selectionCommun. Stat. Theory Methods199019205219106040910.1080/03610929008830198 BhushanSGuptaRSearls’ ratio product type estimatorsInt. J. Stat. Syst.2019142937 Mahdizadeh, M. and Zamanzade, E. (2018). Smooth estimation of a reliability function in ranked set sampling. Stat. J. Theor. Appl. Stat. Khan, L., Shabbir, J. and Khalil, A. (2019). A new class of regression cum ratio estimators of population mean in ranked set sampling. Life Cycle Reliab. Saf. Eng. , 1–4. ZamanzadeEMahdizadehMEstimating the population proportion in pair ranked set sampling with application to air quality monitoringJ. Appl. Stat.201845426437376473510.1080/02664763.2017.1279596 BhushanSGuptaRSome new log-type class of double sampling estimatorsInt. J. Appl. Agric. Res.2019143140 ShahzadUPerriPFHanifMA new class of ratio-type estimators for improving mean estimation of nonsensitive and sensitive variables by using supplementary informationCommun. Stat. Simul. Comput.20184825662585400122110.1080/03610918.2018.1458133 ZamanzadeEMahdizadehMA more efficient proportion estimator in ranked set samplingStat. Probab. Lett.20171292833368851110.1016/j.spl.2017.05.001 BhushanSGuptaRA class of log-type estimators for population mean using auxiliary information on an attribute and a variable using double sampling techniqueInt. J. Comput. Appl. Math.201914110 PLH Yu (265_CR43) 1997; 53 N Koyuncu (265_CR17) 2009; 139 C Kadilar (265_CR14) 2003; 45 265_CR12 265_CR34 265_CR35 265_CR10 265_CR32 265_CR33 N Mehta (265_CR20) 2016; 45 265_CR31 LN Upadhyaya (265_CR41) 1985; 39 U Shahzad (265_CR30) 2018; 48 HA Muttlak (265_CR25) 1995; 37 S Bhushan (265_CR6) 2019; 14 E Zamanzade (265_CR45) 2018; 45 GA McIntyre (265_CR19) 1952; 3 S Bhushan (265_CR3) 2019; 12 HM Samawi (265_CR27) 1996; 38 HP Singh (265_CR37) 2003; 52 LN Upadhyaya (265_CR42) 1999; 41 265_CR1 BVS Sisodia (265_CR39) 1981; 33 E Zamanzade (265_CR46) 2020; 29 HA Muttlak (265_CR23) 1990; 19 265_CR4 CE Sarndal (265_CR28) 2003 S Bhushan (265_CR9) 2020; 28 TR Dell (265_CR11) 1972; 28 E Zamanzade (265_CR44) 2017; 129 K Takahasi (265_CR40) 1968; 20 265_CR22 C Kadilar (265_CR15) 2009; 50 LS Halls (265_CR13) 1966; 12 265_CR8 S Bhushan (265_CR5) 2019; 14 S Singh (265_CR29) 2003 265_CR18 B Prasad (265_CR26) 1989; 18 M Khoshnevisan (265_CR16) 2007; 22 S Bhushan (265_CR7) 2019; 14 M Mahdizadeh (265_CR21) 2016; 1 HP Singh (265_CR38) 2014; 84 HP Singh (265_CR36) 1998; 48 S Bhushan (265_CR2) 2015; 11 HA Muttlak (265_CR24) 1992; 34 |
| References_xml | – reference: Shahzad, U., Al-Noor, N.H., Hanif, M. and Sajjad, I. (2020a). An exponential family of median based estimators for mean estimation with simple random sampling scheme. Commun. Stat. Theory Methods. https://doi.org/10.1080/03610926.2020.1725828. – reference: Bhushan, S. and Gupta, R. (2019b). An improved log-type family of estimators using attribute. J. Stat. Manag. Syst.https://doi.org/10.1080/09720510.1661604. – reference: PrasadBSome improved ratio type estimators of population mean and ratio in finite population sample surveysCommun. Stat. Theory Methods19891837939298591310.1080/03610928908829905 – reference: KhoshnevisanMSinghRChauhanPSawanNSmarandacheFA general family of estimators for estimating population mean using known value of some population parameter(s)Far East J. Theor. Stat.20072218119123567731133.62005 – reference: KoyuncuNKadilarCRatio and product estimator in stratified random samplingJ. Stat. Plan. Infer.200913925522558252364710.1016/j.jspi.2008.11.009 – reference: KadilarCUnyaziciYCingiHRatio estimator for the population mean using ranked set samplingStat. Pap.200950301309247618910.1007/s00362-007-0079-y – reference: MuttlakHAParameter estimation in simple linear regression using ranked set samplingBiom. J.19953779981010.1002/bimj.4710370704 – reference: ZamanzadeEMahdizadehMEstimating the population proportion in pair ranked set sampling with application to air quality monitoringJ. Appl. Stat.201845426437376473510.1080/02664763.2017.1279596 – reference: MahdizadehMZamanzadeEKernel-based estimation of P(X > Y ) in ranked set samplingSORT-Stat. Oper. Res. Trans.2016124326635924891356.62063 – reference: SinghSAdvanced sampling theory with applications: How Michael selected Amy, 1&22003The NetherlandsKluwer10.1007/978-94-007-0789-4 – reference: BhushanSKumarALog type estimators of population mean under ranked set samplingPredictive Analytics Stat. Big Data Concepts Model.202028477410.2174/9789811490491120010007http://dx.doi.org/10.2174/9789811490491120010007 – reference: SinghHPEspejoMROn linear regression and ratio estimator using coefficient of variation of auxiliary variateStatistician20035259671973882 – reference: BhushanSGuptaRA class of log-type estimators for population mean using auxiliary information on an attribute and a variable using double sampling techniqueInt. J. Comput. Appl. Math.201914110 – reference: Mahdizadeh, M. and Zamanzade, E. (2018). Smooth estimation of a reliability function in ranked set sampling. Stat. J. Theor. Appl. Stat. – reference: MuttlakHAMcDonaldLLRanked set sampling and line intercept method: A more efficient procedureBiom. J.19923432934610.1002/bimj.4710340307 – reference: McIntyreGAA method of unbiased selective sampling using ranked setAust. J. Agr. Res.1952338539010.1071/AR9520385 – reference: TakahasiKWakimotoKOn unbiased estimates of the population mean based on the sample stratified by means of orderingAnn. Inst. Stat. Math.19682013110.1007/BF02911622 – reference: BhushanSGuptaRSome new log-type class of double sampling estimatorsInt. J. Appl. Agric. Res.2019143140 – reference: Bhushan, S. and Kumar, A (2020a). On optimal classes of estimators under ranked set sampling. Commun. Stat. Theory Methods. https://doi.org/10.1080/03610926.2020.1777431. – reference: Dell, T.R. (1969). The theory and some applications of ranked set sampling (Doctoral dissertation) University of Georgia, Athens, GA. – reference: UpadhyayaLNSinghHPUse of transformed auxiliary variable in estimating the finite population meanBiom. J.199941627636172023210.1002/(SICI)1521-4036(199909)41:5<627::AID-BIMJ627>3.0.CO;2-W – reference: Shahzad, U., Al-Noor, N.H., Hanif, M., Sajjad, I. and Anas, M.M. (2020b), Imputation based mean estimators in case of missing data utilizing robust regression and variance-covariance matrices. Commun. Stat. Simul. Comput.https://doi.org/10.1080/03610918.2020.1740266. – reference: MuttlakHAMcDonaldLLRanked set sampling with respect to a concomitant variables and with size biased probability of selectionCommun. Stat. Theory Methods199019205219106040910.1080/03610929008830198 – reference: Singh, H.P. and Kakran, M.S. (1993). A modified ratio estimator using known coefficient of kurtosis of an auxiliary character. In: Advanced sampling theory with applications (S. Singh, H.P. Singh, and M.S. Kakran, eds), vol. 2. Kluwer Academic Publishers, Kluwer. – reference: ZamanzadeEMahdizadehMUsing ranked set sampling with extreme ranks in estimating the population proportionStat. Methods Med. Res.202029165177405512910.1177/0962280218823793 – reference: YuPLHLamKRegression estimator in ranked set samplingBiometrics1997531070108010.2307/2533564 – reference: Khan, L., Shabbir, J. and Khalil, A. (2019). A new class of regression cum ratio estimators of population mean in ranked set sampling. Life Cycle Reliab. Saf. Eng. , 1–4. – reference: SarndalCESwenssonBWretmanJModel assisted survey sampling2003New YorkSpringer1027.62004 – reference: DellTRClutterJLRanked set sampling theory with order statistics backgroundBiometrics19722854555510.2307/2556166 – reference: MehtaNMandowaraVLA modified ratio-cum-product estimator of finite population mean using ranked set samplingCommun. Stat. Theory Methods201645267276344791310.1080/03610926.2013.830748 – reference: KadilarCCingiHRatio estimators in stratified random samplingBiom. J200345218225196594610.1002/bimj.200390007 – reference: SinghHPTailorRSinghSGeneral procedure for estimating the population mean using ranked set samplingJ. Stat. 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| Title | Novel Log Type Class Of Estimators Under Ranked Set Sampling |
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