×
Ozturk, Omer; Balakrishnan, Narayanaswamy

Constructing quantile confidence intervals using extended simple random sample in finite populations. (English) Zbl 1418.62207

Statistics 53, No. 4, 792-806 (2019).
Summary: This paper constructs quantile confidence intervals based on extended simple random sample (SRS) from a finite population, where ranks of population units are all known. Extended simple random sample borrows additional information from unmeasured observations in the population by conditioning on the population ranks of the measured units in SRS. The confidence intervals are improved using Rao-Blackwell theorem over the conditional distribution of sample ranks given the measured sample units. Empirical evidence shows that the proposed confidence intervals have shorter lengths than confidence intervals constructed from an SRS sample.

Cited in 1 Document

MSC:

62G15 Nonparametric tolerance and confidence regions
62G30 Order statistics; empirical distribution functions
62D05 Sampling theory, sample surveys

Keywords:

Rao-Blackwell theorem; inner quantiles; outer quantiles; ranked set sample; judgment post stratified sample

Software:

isotone
Cite Review PDF
Full Text: DOI

References:

[1] Sedransk, J.; Meyer, J., Confidence intervals for the quantiles of a finite population: Simple random and stratified simple random sampling, J Roy Stat Soc, 40, 239-252 (1978) · Zbl 0386.62009
[2] Takahasi, K.; Futatsuya, M., Ranked set sampling from a finite population, Proc Inst Statist Math, 36, 55-68 (1988)
[3] Patil, Gp; Sinha, Ak; Taillie, C., Finite population correction for ranked set sampling, Annal Inst Stat Math, 47, 621-636 (1995) · Zbl 0843.62013 · doi:10.1007/BF01856537
[4] Deshpande, Jv; Frey, J.; Ozturk, O., Nonparametric ranked-set sampling confidence intervals for a finite population, Environm Ecolog Stat, 13, 25-40 (2006) · doi:10.1007/s10651-005-5688-9
[5] Frey, J., Recursive computation of inclusion probabilities in ranked set sampling, J Stat Plan Infer, 141, 3632-3639 (2011) · Zbl 1221.62017 · doi:10.1016/j.jspi.2011.05.017
[6] Jafari Jozani, M.; Johnson, Bc., Design based estimation for ranked set sampling in finite population, Environm Ecolog Stat, 18, 663-685 (2011) · doi:10.1007/s10651-010-0156-6
[7] Ozturk, O.; Jafari Jozani, M., Inclusion probabilities in partially rank ordered set sampling, Comput Stat Data Anal, 69, 122-132 (2013) · Zbl 1471.62154 · doi:10.1016/j.csda.2013.07.034
[8] Al-Saleh, Mf; Samawi, Hm., A note on inclusion probability in ranked set sampling and some of its variations, Test, 16, 198-209 (2007) · Zbl 1119.62009 · doi:10.1007/s11749-006-0009-7
[9] Gokpinar, F.; Ozdemir, Ya., Generalization of inclusion probabilities in ranked set sampling, Hacettepe J Math Stat, 39, 89-95 (2010) · Zbl 1194.62011
[10] Ozturk, O., Estimation of population mean and total in finite population setting using multiple auxiliary variables, J Agric Biol Environm Stat, 19, 161-184 (2014) · Zbl 1303.62089 · doi:10.1007/s13253-013-0163-9
[11] Ozturk, O., Estimation of a finite population mean and total using population ranks of sample units, J Agric Biol Environm Stat, 21, 181-202 (2016) · Zbl 1342.62178 · doi:10.1007/s13253-015-0231-4
[12] Ozturk, O., Statistical inference based on judgment post-stratified samples in finite population, Survey Meth, 42, 239-262 (2016)
[13] Ozturk, O., Two-stage cluster samples with ranked set sampling designs, Annal Inst Stat Math., 71, 63-91 (2019) · Zbl 1415.62002 · doi:10.1007/s10463-017-0623-z
[14] Ozturk, O., Ratio estimators based on a ranked set sample in a finite population setting, J Korean Stat Soc., 47, 226-238 (2018) · Zbl 1390.62013 · doi:10.1016/j.jkss.2018.02.001
[15] Samawi, Hm; Muttlak, Ha., Estimation of ratio using ranked set sampling, Biom J, 38, 753-764 (1996) · Zbl 0929.62005 · doi:10.1002/bimj.4710380616
[16] Nematollahi, N.; Salehi, Mm; Aliakbari Saba, R., Two-stage cluster sampling with ranked set sampling in the secondary sampling frame, Commun Stat Theory Method, 37, 2402-2415 (2008) · Zbl 1143.62009 · doi:10.1080/03610920801919684
[17] Sud, V.; Mishra, Dc., Estimation of finite population mean using ranked set two stage sampling designs, J Indian Soc Agric Stat, 60, 108-117 (2006) · Zbl 1188.62096
[18] Wang, X.; Lim, J.; Stokes, L., Using ranked set sampling with cluster randomized designs for improved inference on treatment effects, J Am Stat Assoc, 516, 1576-1590 (2016) · doi:10.1080/01621459.2015.1093946
[19] Omidvar, S.; Jafari Jozani, M.; Nematollahi, N., Judgment post-stratification in finite mixture modeling: An example in estimating the prevalence of osteoporosis, Stat Med, 37, 4823-4836 (2018)
[20] Zamanzade, E.; Wang, X., Estimation of population proportion for judgment post-stratification, Comput Stat Data Anal, 112, 257-269 (2017) · Zbl 1464.62194 · doi:10.1016/j.csda.2017.03.016
[21] Meyer, Js., Outer and inner confidence intervals for finite population quantile intervals, J Ame Stat Assoc, 82, 201-204 (1987) · Zbl 0607.62051 · doi:10.1080/01621459.1987.10478420
[22] Roy, D., The discrete normal distribution, Commun Stat Theory Method, 32, 1871-1883 (2003) · Zbl 1155.60302 · doi:10.1081/STA-120023256
[23] De Leeuw, J.; Hornik, K.; Mair, P., Isotone optimization in r: pool-adjacent-violators algorithm (PAVA) and active set methods, J Stat Softw, 32, 1-24 (2009) · doi:10.18637/jss.v032.i05
[24] Kadilar, C.; Cingi, H., Ratio estimators in stratified random sampling, Biom J, 45, 218-225 (2003) · Zbl 1441.62391 · doi:10.1002/bimj.200390007
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.