Modified classes of estimators in circular systematic sampling
Year 2017,
Volume: 46 Issue: 4, 743 - 765, 01.08.2017
Saba Riaz
,
Giancarlo Diana
Javid Shabbir
Abstract
In this paper we consider the problem of estimation of population mean in circular systematic sampling design along with the non-response
problem. For the population mean using auxiliary information three generalized classes of estimators are suggested. The biases and the mean square errors of the suggested classes of estimators are obtained and compared with sample mean, linear regression estimators, [23] estimator and [21] estimators. A numerical study is provided to Show that the proposed classes of estimators based on circular systematic design can be more efficient than the estimators based on simple random sampling. Moreover, a simulation study is accomplished when some population parameters are assumed to be unknown.
References
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Estimation of the Headcount Index, Social Indicators Research DOI 10.1007/s11205-014-
0757-9, 2014.
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Economic Quality Control 27, 195208, 2012.
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auxiliary information in systematic sampling, Journal of Statistical Theory and Practice 6,
274285, 2012.
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auxiliary information, Communication in Statistics-Theory and Methods 42, 145163, 2013.
- Singh, P., Jindal, K. K. and Garg, J. N. On modified systematic sampling, Biometrika 55,
541546, 1968.
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ratio-type estimators in systematic sampling, Journal of Reliability and Statistical Studies
5(1), 7382, 2012.
- Singh, R. and Singh, H. P. Almost unbiased ratio and product-type estimators in systematic
sampling, QUESTIIO 22(3), 403416, 1998.
- Riaz, S., Diana, G. and Shabbir, J. Improved classes of estimators for population mean in
presence of non-response, Pakistan Journal of Statistics 30(1), 83100, 2014.
- Uthayakumaran, N. Additional circular systematic sampling methods, Biometrical Journal
40(4), 467474, 1998.
- Verma, H., Singh, R. D. and Singh, R. A general class of regression type estimators in
systematic sampling under non-response, Octogon Mathematical Magazine 20(2), 542550,
2012.
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under non-response, National Academy Science Letters 37(1), 9195, 2014.
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345377, 1948.
Year 2017,
Volume: 46 Issue: 4, 743 - 765, 01.08.2017
Saba Riaz
,
Giancarlo Diana
Javid Shabbir
References
- Berger, Y. G. and Muñoz, J. F. On estimating quantiles using auxiliary information, Journal
of Ocial Statistics 31(1), 101119, 2015.
- Cochran, W. G. Sampling Techniques, (New York, Wiley, 1977).
- Diana, G. and Giordan, M. and Perri, P. F. An improved class of estimators for the popu-
lation mean, Statistical Methods and Applications 20, 123140, 2011.
- Diana, G. and Riaz, S. and Shabbir, J. Hansen and Hurwitz estimator with scrambled
response on the second call, Journal of Applied Statistics 41(3), 596611, 2014.
- Gautschi, W. Some remarks on systematic sampling, The Annals of Mathematical Statistics
28, 385394, 1957.
- Harms, T. and Duchesne, P. On Calibration estimation for quantiles, Survey Methdology
32, 3752, 2006.
- Hajeck, J. Optimum strategy and other problems in probability sampling, Cosopis pro Pestovani
Mathematiky 84, 387423, 1959.
- Hansen, M. H. and Hurwitz, W. N. The problems of non-response in sample surveys, Journal
of American Statistical Association 41, 517529, 1946.
- Koyuncu, N. and Kadilar, C. Ecient estimators for the population mean, Hacettepe Journal
of Mathematics and Statistics 38, 217233, 2009.
- Lahiri, D. B. A method for selection providing unbiased estimates, Bulletin of the International
Statistical Institute 33(2), 133140, 1951.
- Leu, C.H. and Kao, F. F. Modied balanced circular systematic sampling, Statistics and
Probability Letters 76, 373383, 2006.
- Leu, C.H. and Tsui, K. W. New partially systematic sampling, Statistica Sinica 6, 617630,
1996.
- Madow, W. G. On the theory of systematic sampling, The Annals of Mathematical Statistics
24, 101106, 1953.
- Muñoz, J. F., ÁlvarezVerdejo, E., GarcíaFernández, R. M. and Barroso, L. J. Ecient
Estimation of the Headcount Index, Social Indicators Research DOI 10.1007/s11205-014-
0757-9, 2014.
- Okafor, F. C. and Lee, H. Double sampling for ratio and regression estimation with sub-
sampling the non-respondents, Survey Methodology, 26(2), 183188, 2000.
- Rao, J. N. K, Kovar, J. G. and Mantel, H. J. On estimating distribution functions and
quantiles from survey data using auxilairy information, Bimetrika 77, 365375, 1990.
- Sengupta, S. and Chattophyadhyay, S. A note on circular systematic sampling, Sankhya B
49, 186187, 1987.
- Sethi, V. K. On optimum pairing of units, Sankhya B 27, 315320.
- Singh, H. P. and Jatwa, N. K. A class of exponential-type estimators in systematic sampling,
Economic Quality Control 27, 195208, 2012.
- Singh, H. P. and Solanki, R. S. An efficient class of estimators for the population mean using
auxiliary information in systematic sampling, Journal of Statistical Theory and Practice 6,
274285, 2012.
- Singh, H. P. and Solanki, R. S. An efficient class of estimators for the population mean using
auxiliary information, Communication in Statistics-Theory and Methods 42, 145163, 2013.
- Singh, P., Jindal, K. K. and Garg, J. N. On modified systematic sampling, Biometrika 55,
541546, 1968.
- Singh, R., Malik, S., Chaudry, M. K., Verma, H. K. and Adewara, A. A. A general family of
ratio-type estimators in systematic sampling, Journal of Reliability and Statistical Studies
5(1), 7382, 2012.
- Singh, R. and Singh, H. P. Almost unbiased ratio and product-type estimators in systematic
sampling, QUESTIIO 22(3), 403416, 1998.
- Riaz, S., Diana, G. and Shabbir, J. Improved classes of estimators for population mean in
presence of non-response, Pakistan Journal of Statistics 30(1), 83100, 2014.
- Uthayakumaran, N. Additional circular systematic sampling methods, Biometrical Journal
40(4), 467474, 1998.
- Verma, H., Singh, R. D. and Singh, R. A general class of regression type estimators in
systematic sampling under non-response, Octogon Mathematical Magazine 20(2), 542550,
2012.
- Verma, H., Singh, R. D. and Singh, R. Some improved estimators in systematic sampling
under non-response, National Academy Science Letters 37(1), 9195, 2014.
- Wolter, K. M. Introduction to Variance Estimation, (Springer, New York, 1985).
- Yates, F. Systematic sampling, Philosophical Transactions Royal Society, London, A 241,
345377, 1948.