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Modified classes of estimators in circular systematic sampling

Year 2017, Volume: 46 Issue: 4, 743 - 765, 01.08.2017

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

  • 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.
Year 2017, Volume: 46 Issue: 4, 743 - 765, 01.08.2017

Abstract

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.
There are 30 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Statistics
Authors

Saba Riaz

Giancarlo Diana This is me

Javid Shabbir

Publication Date August 1, 2017
Published in Issue Year 2017 Volume: 46 Issue: 4

Cite

APA Riaz, S., Diana, G., & Shabbir, J. (2017). Modified classes of estimators in circular systematic sampling. Hacettepe Journal of Mathematics and Statistics, 46(4), 743-765.
AMA Riaz S, Diana G, Shabbir J. Modified classes of estimators in circular systematic sampling. Hacettepe Journal of Mathematics and Statistics. August 2017;46(4):743-765.
Chicago Riaz, Saba, Giancarlo Diana, and Javid Shabbir. “Modified Classes of Estimators in Circular Systematic Sampling”. Hacettepe Journal of Mathematics and Statistics 46, no. 4 (August 2017): 743-65.
EndNote Riaz S, Diana G, Shabbir J (August 1, 2017) Modified classes of estimators in circular systematic sampling. Hacettepe Journal of Mathematics and Statistics 46 4 743–765.
IEEE S. Riaz, G. Diana, and J. Shabbir, “Modified classes of estimators in circular systematic sampling”, Hacettepe Journal of Mathematics and Statistics, vol. 46, no. 4, pp. 743–765, 2017.
ISNAD Riaz, Saba et al. “Modified Classes of Estimators in Circular Systematic Sampling”. Hacettepe Journal of Mathematics and Statistics 46/4 (August 2017), 743-765.
JAMA Riaz S, Diana G, Shabbir J. Modified classes of estimators in circular systematic sampling. Hacettepe Journal of Mathematics and Statistics. 2017;46:743–765.
MLA Riaz, Saba et al. “Modified Classes of Estimators in Circular Systematic Sampling”. Hacettepe Journal of Mathematics and Statistics, vol. 46, no. 4, 2017, pp. 743-65.
Vancouver Riaz S, Diana G, Shabbir J. Modified classes of estimators in circular systematic sampling. Hacettepe Journal of Mathematics and Statistics. 2017;46(4):743-65.