Published

2015-01-01

Estimation of Population Mean in the Presence of Non-Response and Measurement Error

Estimacion de la media poblacional con presencia de errores de medición y no respuesta

DOI:

https://doi.org/10.15446/rce.v38n1.48807

Keywords:

Estimation, Mean Squared Error, Measurement Error, Nonresponse, Ratio Estimator, Sampling Error (en)
Error cuadrático medio, Error de medición, Error de muestreo, Estimación, Estimador de razón. (es)

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Authors

  • Sunil Kumar Alliance University, Bangalore, India
  • Sandeep Bhogal Shri Mata Vaishno Devi University, Kakryal, India
  • N. S. Nataraja Alliance University, Bangalore, India
  • M. Viswanathaiah Alliance University, Bangalore, India

Under classical survey sampling theory the errors mainly studied in the estimation are sampling errors. However, often non-sampling errors are more influential to the properties of the estimator than sampling errors. This is recognized by practitioners, researchers and many great works of literature regarding non-sampling errors have been published during last two decades, especially regarding non-response error which is one of the cornerstones of the non-sampling errors. The literature handles one kind of non-sampling error at a time, although in real surveys more than one non-sampling error is usually present.In this paper, two kinds of non-sampling errors are considered at the estimation stage: non-response and measurement error. An exponential ratio type estimator has been developed to estimate the population mean of the response variable in the presence of non-response and measurement errors. Theoretically and empirically, it has been shown that the proposed estimator is more efficient than usual unbiased estimator and other existing estimators.

En la teoría de muestreo de la encuesta clásica los errores estudiados principalmente en la estimación son el muestreo errores. Sin embargo, a menudo los errores ajenos al muestreo son más influyentes que las propiedades del estimador de errores de muestreo. Esto es reconocido por los profesionales, los investigadores y muchos grandes obras de la literatura en relación con los errores ajenos al muestreo se ha publicado en los últimos dos decenios, especialmente en relación con el error de falta de respuesta, que es una de las piedras angulares de los errores ajenos al muestreo. La literatura se ocupa de un tipo de error no muestral a la vez, aunque en las encuestas reales más de un error no muestral suele estar presente. En este trabajo, dos tipos de errores ajenos al muestreo son considerados en la etapa de la estimación: la falta de respuesta y el error de medición. Un tipo exponencial estimador de razón ha sido desarrollado para estimar la media poblacional de la variable de respuesta en presencia de errores de falta de respuesta y de medición. Teóricamente y empíricamente, se ha mostrado que el estimador propuesto es más eficiente que estimador insesgado habitual y otros estimadores existentes.

https://doi.org/10.15446/rce.v38n1.48807

Estimation of Population Mean in the Presence of Non-Response and Measurement Error

Estimacion de la media poblacional con presencia de errores de medición y no respuesta

SUNIL KUMAR1, SANDEEP BHOUGAL2, N. S. NATARAJA3, M. VISWANATHAIAH4

1Alliance University, Bangalore, India. Assistant Professor. Email: sunilbhougal06@gmail.com
2Shri Mata Vaishno Devi University, School of Mathematics, Kakryal, India. Assistant Professor. Email: sandeep.bhougal@smvdu.ac.in
3Alliance University, Bangalore, India. Assistant Professor. Email: nataraja.ns@alliance.edu.in
4Alliance University, Bangalore, India. Assistant Professor. Email: vmatam@gmail.com

Abstract

Under classical survey sampling theory the errors mainly studied in the estimation are sampling errors. However, often non-sampling errors are more influential to the properties of the estimator than sampling errors. This is recognized by practitioners, researchers and many great works of literature regarding non-sampling errors have been published during last two decades, especially regarding non-response error which is one of the cornerstones of the non-sampling errors. The literature handles one kind of non-sampling error at a time, although in real surveys more than one non-sampling error is usually present.In this paper, two kinds of non-sampling errors are considered at the estimation stage: non-response and measurement error. An exponential ratio type estimator has been developed to estimate the population mean of the response variable in the presence of non-response and measurement errors. Theoretically and empirically, it has been shown that the proposed estimator is more efficient than usual unbiased estimator and other existing estimators.

Key words: Estimation, Mean Squared Error, Measurement Error, Non-response, Ratio Estimator, Sampling Error.

Resumen

En la teoría de muestreo de la encuesta clásica los errores estudiados principalmente en la estimación son el muestreo errores. Sin embargo, a menudo los errores ajenos al muestreo son más influyentes que las propiedades del estimador de errores de muestreo. Esto es reconocido por los profesionales, los investigadores y muchos grandes obras de la literatura en relación con los errores ajenos al muestreo se ha publicado en los últimos dos decenios, especialmente en relación con el error de falta de respuesta, que es una de las piedras angulares de los errores ajenos al muestreo. La literatura se ocupa de un tipo de error no muestral a la vez, aunque en las encuestas reales más de un error no muestral suele estar presente. En este trabajo, dos tipos de errores ajenos al muestreo son considerados en la etapa de la estimación: la falta de respuesta y el error de medición. Un tipo exponencial estimador de razón ha sido desarrollado para estimar la media poblacional de la variable de respuesta en presencia de errores de falta de respuesta y de medición. Teóricamente y empíricamente, se ha mostrado que el estimador propuesto es más eficiente que estimador insesgado habitual y otros estimadores existentes.

Palabras clave: error cuadrático medio, error de medición, error de muestreo, estimación, estimador de razón.

Texto completo disponible en PDF

References

1. Allen, J., Singh, H. & Smarandache, F. (2003), 'A family of estimators of population mean using multi-auxiliary information in presence of measurement errors', International Journal of Social Economics 30, 837-849.

2. Binder, D. A. (2008), Design-based estimation, 'Encyclopedia of Survey Research Methods', SAGE Publications, Inc., p. 192-194. doi: 10.4135/9781412963947.

3. Cochran, W. (1963), Sampling Techniques, John Wiley, New York.

4. Cochran, W. (1977), Sampling Techniques, 3 edn, John Wiley & Sons, Inc., New York.

5. Dixon, J. (2010), Assessing nonresponse bias and measurement error using statistical matching, 'Section on Survey Research Methods - JSM', American Statistical Association, , , p. 3388-3396. *http://www.bls.gov/osmr/pdf/st100190.pdf

6. Dorazio, R. M. (1999), 'Design based and model based inference in surveys of freshwater mollusks', Journal of the North American Benthological Society 18, 118-131.

7. Fuller, W. (1995), 'Estimation in the presence of measurement error', International Statistical Review 63, 121-147.

8. Gregoire, T. G. (1998), 'Design-based and model-based inference in survey sampling: Appreciating the difference', Canadian Journal of Forestry Research 28, 1429-1447.

9. Gregoire, T. G. & Salas, C. (2009), 'Ratio estimation with measurement error in the auxiliary variate', Biometrics 65, 590-598.

10. Groves, R. M. (1989), Survey Errors and Survey Costs, Wiley, New York.

11. Hansen, M. & Hurwitz, W. (1946), 'The problem of non-response in sample surveys', Journal of American Statistical Association 41, 517-529.

12. Ilves, M. (2011), Estimation in the presence of non-response and measurement errors, '', Proceedings of the Third Baltic - Nortic Conference in Survey Statistics, Norrfällsviken, Sweden, p. 13-17.

13. Jackman, S. (1999), 'Correcting surveys for non-response and measurement error using auxiliary information', Electoral Studies 18, 7-27.

14. Khare, B. & Srivastava, S. (1997), 'Transformed ratio type estimators for the population mean in presence of non-response', Communication in Statistics - Theory and Methods 26, 1779-1791.

15. Kish, L. (1954), 'Differentiation in metropolitan areas', American Sociological Review 19, 388-398.

16. Kish, L. (1994), 'Classical and model based estimators for forest inventory', Silva Fennica 28, 3-14.

17. Koch, G. G. & Gillings, D. B. (2006), Inference, design based vs model based, 'Encyclopedia of Statistical Sciences', John Wiley and Sons Inc., New York.

18. Kumar, S., Singh, H., Bhougal, S. & Gupta, R. (2011), 'A class of ratio-cum-product type estimators under double sampling in the presence of non-response', Hacettepe Journal of Mathematics and Statistics 40, 589-599.

19. Manisha, & Singh, R. (2001), 'An estimation of population mean in the presence of measurement errors', Journal of the Indian Society of Agricultural Statistics 54, 13-18.

20. Manisha, & Singh, R. (2002), 'Role of regression estimator involving measurement errors', JBrazilian Journal of Probability and Statistics 16, 39-46.

21. Rao, P. (1986), 'Ratio estimation with sub sampling the non-respondents', Survey Methodology 12, 217-230.

22. Salas, C. & Gregoire, T. (2010), 'Statistical analysis of ratio estimators and their estimators of variances when the auxiliaryvariate is measured with error', European Journal of Forest Research 129, 847-861.

23. Sarndal, C. E., Swensson, B. & Wretman, J. (1992), Model Assisted Survey Sampling', Springer, New York.

24. Shabbir, J., Haq, A. & Gupta, S. (2014), 'A new difference-cum-exponential type estimator of finite population mean in simple random sampling', Revista Colombiana de Estadística 37, 199-211.

25. Shalabh, (1997), 'Ratio method of estimation in the presence of measurement errors', Journal of the Indian Society of Agricultural Statistics 50, 150-155.

26. Sharma, P. & Singh, R. (2013), 'A generalized class of estimators for finite population variance in presence of measurement errors', Journal of Modern Applied Statistical Methods 12, 231-241.

27. Shukla, D., Pathak, S. & Thakue, N. S. (2012), 'Class(es) of factor-type estimator(s) in presence of measurement error', Journal of Modern Applied Statistical Methods 11, 336-347.

28. Shukla, D., Pathak, S. & Thakur, N. (2012), 'An estimator for mean estimation in presence of measurement error', Research and Reviews: A Journal of Statistics 1, 1-8.

29. Singh, H. & Karpe, N. (2007), 'Effect of measurement errors on a class of estimators of population mean using auxiliary information in sample surveys', Journal of Statistical Research of Iran 4, 175-189.

30. Singh, H. & Karpe, N. (2008), 'Estimation of population variance using auxiliary information in the presence of measurement errors', Statistics in Transition-New Series 9, 443-470.

31. Singh, H. & Karpe, N. (2009), 'On the estimation of ratio and product of two population means using supplementary information in presence of measurement errors', Statistica, Anno 69, 27-47.

32. Singh, H. & Karpe, N. (2010), 'Estimation of mean, ratio and product using auxiliary information in the presence of measurement errors in sample surveys', Journal of Statistical Theory and Practice 4, 111-136.

33. Singh, H. & Kumar, S. (2008), 'A regression approach to the estimation of the finite population mean in the presence of non-response', Australian and New Zealand Journal of Statistics 50, 395-408.

34. Wang, L. (2002), 'A simple adjustment for measurement errors in some dependent variable models', Statistics & Probability Letters 58, 427-433.

[Recibido en enero de 2014. Aceptado en septiembre de 2014]

Este artículo se puede citar en LaTeX utilizando la siguiente referencia bibliográfica de BibTeX:

@ARTICLE{RCEv38n1a08,
    AUTHOR  = {Kumar, Sunil and Bhougal, Sandeep and Nataraja, N. S. and Viswanathaiah, M.},
    TITLE   = {{Estimation of Population Mean in the Presence of Non-Response and Measurement Error}},
    JOURNAL = {Revista Colombiana de Estadística},
    YEAR    = {2015},
    volume  = {38},
    number  = {1},
    pages   = {145-161}
}

References

Allen, J., Singh, H. & Smarandache, F. (2003), ‘A family of estimators of population mean using multi-auxiliary information in presence of measurement errors’, International Journal of Social Economics 30, 837–849.

Binder, D. A. (2008), Design-based estimation, in P. J. Lavrakas, ed., ‘Encyclopedia of Survey Research Methods’, SAGE Publications, Inc., pp. 192–194. doi:10.4135/9781412963947.

Cochran, W. (1963), Sampling Techniques, John Wiley, New York.

Cochran, W. (1977), Sampling Techniques, 3 edn, John Wiley & Sons, Inc., New York.

Dixon, J. (2010), Assessing nonresponse bias and measurement error using statistical matching, in R. Harter, ed., ‘Section on Survey Research Methods –JSM’, American Statistical Association, pp. 3388–3396.

*http://www.bls.gov/osmr/pdf/st100190.pdf

Dorazio, R. M. (1999), ‘Design based and model based inference in surveys of freshwater mollusks’, Journal of the North American Benthological Society 18, 118–131.

Fuller, W. (1995), ‘Estimation in the presence of measurement error’, International Statistical Review 63, 121–147.

Gregoire, T. G. (1998), ‘Design-based and model-based inference in survey sampling: Appreciating the difference’, Canadian Journal of Forestry Research 28, 1429–1447.

Gregoire, T. G. & Salas, C. (2009), ‘Ratio estimation with measurement error in the auxiliary variate’, Biometrics 65, 590–598.

Groves, R. M. (1989), Survey Errors and Survey Costs, Wiley, New York.

Hansen, M. & Hurwitz, W. (1946), ‘The problem of non-response in sample surveys’, Journal of American Statistical Association 41, 517–529.

Ilves, M. (2011), Estimation in the presence of non-response and measurement errors, Proceedings of the Third Baltic – Nortic Conference in Survey Statistics, Norrfällsviken, Sweden, pp. 13–17.

Jackman, S. (1999), ‘Correcting surveys for non-response and measurement error using auxiliary information’, Electoral Studies 18, 7–27.

Khare, B. & Srivastava, S. (1997), ‘Transformed ratio type estimators for the population mean in presence of non-response’, Communication in Statistics – Theory and Methods 26, 1779–1791.

Kish, L. (1954), ‘Differentiation in metropolitan areas’, American Sociological Review 19, 388–398.

Kish, L. (1994), ‘Classical and model based estimators for forest inventory’, Silva Fennica 28, 3–14.

Koch, G. G. & Gillings, D. B. (2006), Inference, design based vs model based, in S. Kotz, C. B. Read, N. Balakrishnan & B. Vidakovic, eds, ‘Encyclopedia of Statistical Sciences’, John Wiley and Sons Inc., New York.

Kumar, S., Singh, H., Bhougal, S. & Gupta, R. (2011), ‘A class of ratio-cumproduct type estimators under double sampling in the presence of nonresponse’, Hacettepe Journal of Mathematics and Statistics 40, 589–599.

Manisha & Singh, R. (2001), ‘An estimation of population mean in the presence of measurement errors’, Journal of the Indian Society of Agricultural Statistics 54, 13–18.

Manisha & Singh, R. (2002), ‘Role of regression estimator involving measurement errors’, JBrazilian Journal of Probability and Statistics 16, 39–46.

Rao, P. (1986), ‘Ratio estimation with sub sampling the non-respondents’, Survey Methodology 12, 217–230.

Salas, C. & Gregoire, T. (2010), ‘Statistical analysis of ratio estimators and their estimators of variances when the auxiliaryvariate is measured with error’, European Journal of Forest Research 129, 847–861.

Sarndal, C. E., Swensson, B. & Wretman, J. (1992), Model Assisted Survey Sampling’,Springer, New York.

Shabbir, J., Haq, A. & Gupta, S. (2014), ‘A new difference-cum-exponential type estimator of finite population mean in simple random sampling’, Revista Colombiana de Estadística 37, 199–211.

Shalabh (1997), ‘Ratio method of estimation in the presence of measurement errors’, Journal of the Indian Society of Agricultural Statistics 50, 150–155.

Sharma, P. & Singh, R. (2013), ‘A generalized class of estimators for finite population variance in presence of measurement errors’, Journal of Modern Applied Statistical Methods 12, 231–241.

Shukla, D., Pathak, S. & Thakue, N. S. (2012), ‘Class(es) of factor-type estimator(s) in presence of measurement error’, Journal of Modern Applied Statistical Methods 11, 336–347.

Shukla, D., Pathak, S. & Thakur, N. (2012), ‘An estimator for mean estimation in presence of measurement error’, Research and Reviews: A Journal of Statistics 1, 1–8.

Singh, H. & Karpe, N. (2007), ‘Effect of measurement errors on a class of estimators of population mean using auxiliary information in sample surveys’, Journal of Statistical Research of Iran 4, 175–189.

Singh, H. & Karpe, N. (2008), ‘Estimation of population variance using auxiliary information in the presence of measurement errors’, Statistics in Transition- New Series 9, 443–470.

Singh, H. & Karpe, N. (2009), ‘On the estimation of ratio and product of two population means using supplementary information in presence of measurement errors’, Statistica, Anno 69, 27–47.

Singh, H. & Karpe, N. (2010), ‘Estimation of mean, ratio and product using auxiliary information in the presence of measurement errors in sample surveys’, Journal of Statistical Theory and Practice 4, 111–136.

Singh, H. & Kumar, S. (2008), ‘A regression approach to the estimation of the finite population mean in the presence of non-response’, Australian and New Zealand Journal of Statistics 50, 395–408.

Wang, L. (2002), ‘A simple adjustment for measurement errors in some dependent variable models’, Statistics & Probability Letters 58, 427–433.

How to Cite

APA

Kumar, S., Bhogal, S., Nataraja, N. S. and Viswanathaiah, M. (2015). Estimation of Population Mean in the Presence of Non-Response and Measurement Error. Revista Colombiana de Estadística, 38(1), 145–161. https://doi.org/10.15446/rce.v38n1.48807

ACM

[1]
Kumar, S., Bhogal, S., Nataraja, N.S. and Viswanathaiah, M. 2015. Estimation of Population Mean in the Presence of Non-Response and Measurement Error. Revista Colombiana de Estadística. 38, 1 (Jan. 2015), 145–161. DOI:https://doi.org/10.15446/rce.v38n1.48807.

ACS

(1)
Kumar, S.; Bhogal, S.; Nataraja, N. S.; Viswanathaiah, M. Estimation of Population Mean in the Presence of Non-Response and Measurement Error. Rev. colomb. estad. 2015, 38, 145-161.

ABNT

KUMAR, S.; BHOGAL, S.; NATARAJA, N. S.; VISWANATHAIAH, M. Estimation of Population Mean in the Presence of Non-Response and Measurement Error. Revista Colombiana de Estadística, [S. l.], v. 38, n. 1, p. 145–161, 2015. DOI: 10.15446/rce.v38n1.48807. Disponível em: https://revistas.unal.edu.co/index.php/estad/article/view/48807. Acesso em: 24 apr. 2024.

Chicago

Kumar, Sunil, Sandeep Bhogal, N. S. Nataraja, and M. Viswanathaiah. 2015. “Estimation of Population Mean in the Presence of Non-Response and Measurement Error”. Revista Colombiana De Estadística 38 (1):145-61. https://doi.org/10.15446/rce.v38n1.48807.

Harvard

Kumar, S., Bhogal, S., Nataraja, N. S. and Viswanathaiah, M. (2015) “Estimation of Population Mean in the Presence of Non-Response and Measurement Error”, Revista Colombiana de Estadística, 38(1), pp. 145–161. doi: 10.15446/rce.v38n1.48807.

IEEE

[1]
S. Kumar, S. Bhogal, N. S. Nataraja, and M. Viswanathaiah, “Estimation of Population Mean in the Presence of Non-Response and Measurement Error”, Rev. colomb. estad., vol. 38, no. 1, pp. 145–161, Jan. 2015.

MLA

Kumar, S., S. Bhogal, N. S. Nataraja, and M. Viswanathaiah. “Estimation of Population Mean in the Presence of Non-Response and Measurement Error”. Revista Colombiana de Estadística, vol. 38, no. 1, Jan. 2015, pp. 145-61, doi:10.15446/rce.v38n1.48807.

Turabian

Kumar, Sunil, Sandeep Bhogal, N. S. Nataraja, and M. Viswanathaiah. “Estimation of Population Mean in the Presence of Non-Response and Measurement Error”. Revista Colombiana de Estadística 38, no. 1 (January 1, 2015): 145–161. Accessed April 24, 2024. https://revistas.unal.edu.co/index.php/estad/article/view/48807.

Vancouver

1.
Kumar S, Bhogal S, Nataraja NS, Viswanathaiah M. Estimation of Population Mean in the Presence of Non-Response and Measurement Error. Rev. colomb. estad. [Internet]. 2015 Jan. 1 [cited 2024 Apr. 24];38(1):145-61. Available from: https://revistas.unal.edu.co/index.php/estad/article/view/48807

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CrossRef citations17

1. Ahmed Audu, Rajesh Singh, Supriya Khare, N. S. Dauran. (2021). Almost unbiased estimators for population mean in the presence of non-response and measurement error. Journal of Statistics and Management Systems, 24(3), p.573. https://doi.org/10.1080/09720510.2020.1759209.

2. Nujayma M. A. Salim, Christopher O. Onyango. (2022). A Modified Regression Estimator for Single Phase Sampling in the Presence of Observational Errors. Open Journal of Statistics, 12(02), p.175. https://doi.org/10.4236/ojs.2022.122012.

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6. G. N. Singh, D. Bhattacharyya, A. Bandyopadhyay. (2021). Some logarithmic and sine-type imputation techniques for missing data in survey sampling in the presence of measurement errors. Journal of Statistical Computation and Simulation, 91(4), p.713. https://doi.org/10.1080/00949655.2020.1828414.

7. G. N. Singh, D. Bhattacharyya, A. Bandyopadhyay. (2022). Formulation of logarithmic type estimators to estimate population mean in successive sampling in presence of random non response and measurement errors. Communications in Statistics - Simulation and Computation, 51(3), p.901. https://doi.org/10.1080/03610918.2019.1659364.

8. Erum Zahid, Javid Shabbir, Osama Abdulaziz Alamri. (2022). A generalized class of estimators for sensitive variable in the presence of measurement error and non-response under stratified random sampling. Journal of King Saud University - Science, 34(2), p.101741. https://doi.org/10.1016/j.jksus.2021.101741.

9. Kuldeep Kumar Tiwari, Sandeep Bhougal, Sunil Kumar, Ronald Onyango, Niansheng Tang. (2022). Assessing the Effect of Nonresponse and Measurement Error Using a Novel Class of Efficient Estimators. Journal of Mathematics, 2022, p.1. https://doi.org/10.1155/2022/4946265.

10. Abdullah Ali H. Ahmadini, Taruna Yadav, S. K. Yadav, Asamh Saleh M. Al Luhayb. (2022). Restructured searls family of estimators of population mean in the presence of nonresponse. Frontiers in Applied Mathematics and Statistics, 8 https://doi.org/10.3389/fams.2022.969068.

11. Muhammad Sajjad, Muhammad Ismail. (2024). Efficient generalized estimators of population mean in the presence of non-response and measurement error. Kuwait Journal of Science, 51(3), p.100224. https://doi.org/10.1016/j.kjs.2024.100224.

12. Shaista Sabir, Aamir Sanaullah. (2022). Efficient Estimation of Mean in Two-Phase Sampling when Measurement Error and Non-Response are Simultaneously Present. Proceedings of the National Academy of Sciences, India Section A: Physical Sciences, 92(4), p.633. https://doi.org/10.1007/s40010-022-00776-x.

13. Muhammad Irfan, Maria Javed, Zhengyan Lin. (2018). Optimized estimation for population mean using conventional and non-conventional measures under the joint influence of measurement error and non-response. Journal of Statistical Computation and Simulation, 88(12), p.2385. https://doi.org/10.1080/00949655.2018.1464571.

14. S. K. Yadav, O. P. Yadav, D. K. Yadav. (2019). Dexterous Estimation of Population Mean in Survey Sampling Under Non-Response Error. International Journal of Mathematical, Engineering and Management Sciences, 4(6), p.1307. https://doi.org/10.33889/IJMEMS.2019.4.6-103.

15. Ahmed Audu, Rajesh Singh, Supriya Khare, N. S. Dauran. (2022). Almost Unbiased Variance Estimators Under the Simultaneous Influence of Non-response and Measurement Errors. Journal of Statistical Theory and Practice, 16(2) https://doi.org/10.1007/s42519-021-00226-8.

16. Erum Zahid, Javid Shabbir, Sat Gupta, Ronald Onyango, Sadia Saeed, Maria Alessandra Ragusa. (2022). A generalized class of estimators for sensitive variable in the presence of measurement error and non-response. PLOS ONE, 17(1), p.e0261561. https://doi.org/10.1371/journal.pone.0261561.

17. Sunil Kumar, Chanda Rani. (2024). Improved estimator for the estimation of sensitive variable using ORRT models. Research in Statistics, 2(1) https://doi.org/10.1080/27684520.2024.2318383.

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