Efficient estimation of population mean in the presence of non-response and measurement error

Kuldeep Kumar Tiwari; Vishwantra Sharma

doi:https://doi.org/10.59170/stattrans-2023-038

Efficient estimation of population mean in the presence of non-response and measurement error

Kuldeep Kumar Tiwari Department of Mathematics, Chandigarh University, Mohali, Punjab, India ORCID:https://orcid.org/0000-0001-5083-1206 , Vishwantra Sharma Directorate of Census Operations, Jammu and Kashmir, India ORCID:https://orcid.org/0000-0001-7387-0670 Statistics in Transition new series, vol. 24, 2023, 3, pages: 95-116 Published online: 13 June 2023 https://doi.org/10.59170/stattrans-2023-038

337 Views 40 Downloads

ARTICLE

(English) PDF

ABSTRACT

In real-world surveys, non-response and measurement errors are common, therefore studying them together seems rational. Some population mean estimators are modified and studied in the presence of non-response and measurement errors. Bias and mean squared error expressions are derived under different cases. For all estimators, a theoretical comparison is made with the sample mean per unit estimator. The Monte-Carlo simulation is used to present a detailed picture of all estimators’ performance.

KEYWORDS

non-response, measurement error, mean squared error, efficiency, mean estimation

REFERENCES

Azeem, M., Hanif, M., (2016). Joint influence of measurement error and non-response on estimation of population mean. Commun Statist. Theory Methods, 14(1), 12. DOI: 10.1080/03610926.2015.1026992.

Bahl, S., Tuteja, R. K., (1991). Ratio and product type exponential estimators. Journal of Information and Optimization Sciences, 12, pp. 159–164.

Cochran,W. G., (1940). The estimation of the yields of cereal experiments by sampling for the ratio gain to total produce. J. Agric. Soc., 30, pp. 262-–275.

Cochran, W. G., (1977). Sampling techniques. New York: Wiley.

Diane, G., Giordan, M., (2012). Finite population variance estimation in presence of measurement errors. Communications in Statistics - Theory and Methods, 41(23), pp. 4302–4314. https://doi.org/10.1080/03610926.2011.573165.

Fuller, W. A., (1987), Measurement Error Models, New York: Wiley.

Gregoire, T. G., Salas, C., (2009). Ratio estimation with measurement error in the auxiliary variate. Biometrics, 65(2), 590—598. DOI:10.1111/j.1541-0420.2008.01110.x.

Hansen, M. H., Hurwitz, W. N., (1946). The problem of non-response in sample surveys. J Amer Statist Assoc, 41, pp. 517–529.

Kumar, S., Bhougal, S., Nataraja, N. S., (2015). Estimation of population mean in the presence of non-response and measurement error. Revista Colombiana de Estadistica, 38(1), pp. 145-–61. DOI:10.15446/rce.v38n1.48807.

Kumar, S., Bhougal, S., (2018). Study on Non Response and Measurement Error using Double Sampling Scheme. J. Stat. Appl. Pro. Lett., 5(1), pp. 43–52.

Kreuter, F., Olson, K., Wagner, J., et al., (2010). Using proxy measure and correlates of survey outcomes to adjust for non-response-examples from multiple surveys. J Royal Statist Soc Ser A, 173(3), pp. 1–21.

Khan, M., Shabbir, J., Hussain, Z., et al., (2014). A Class of Estimators for Finite Population Mean in Double Sampling under Nonresponse Using Fractional Raw Moments. Journal of Applied Mathematics, Volume. http://dx.doi.org/10.1155/2014/282065.

Kadilar, C., Cingi, H., (2004). Ratio estimators in simple random sampling. Applied Mathematics and Computation, 151(3), pp. 893—902. DOI 10.1080/03610926.2019.1682167.

Khare, B. B., Sinha, R. R., (2019). Estimation of product of two population means by multi-auxiliary characters under double sampling the non-respondent. STATISTICS IN TRANSITION new series, 20(3), pp. 81—95. DOI: 10.21307/stattrans-2019-025.

Khare, B. B., Srivastava, S., (1993). Estimation of population mean using auxiliary character in presence of non-response. National Academy of Science and Letters, India, 16(3), pp. 111–114.

Luengo, A. V. G., (2016). Ratio-cum-product estimation in presence of non-response in successive sampling. JAMSI, 12(1), pp. 55–83. https://doi.org/10.1515/jamsi-2016-0005.

Murthy, M. N., (1964). Product method of estimation. Sankhya A, 26, pp. 69—74.

Okafor, F. C., Lee, H., (2000). Double sampling for ratio and regression estimation with sub-sampling the non-respondents. Survey Methodology, 26, pp. 183—188.

Pandey, A. K., Usman, M., Singh, G. N., (2021). Optimality of ratio and regression type estimators using dual of auxiliary variable under non response, Alexandria Engineer ing Journal, 60(5), pp. 4461–4471. https://doi.org/10.1016/j.aej.2021.03.031.

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

Rao, T. J., (1991). On certain methods of improving ratio and regression estimators, Communications in Statistics-Theory and Methods, 20(10), pp. 3325–3340.

Sharma, V., Kumar, S., (2020). Estimation of population mean using transformed auxiliary variable and non-response. Revista Investigacio Operacional, 41(3), pp. 438–444.

Sinha, R. R., Dhingra, H., Thakur, P., (2022). Estimation of Ratio of Two Means Using Regression-Cum-Exponential Estimators in the Presence of Non-response. Proc. Natl. Acad. Sci., India, Sect. A Phys. Sci., 92, pp. 57–64. https://doi.org/10.1007/s40010- 020-00690-0.

Shalabh., (1997). Ratio method of estimation in the presence of measurement errors, Indian Journal of Agricultural Statistics, 50(2), pp. 150–155.

Srivastava, A. K., Shalabh., (2001). Effect of measurement errors on the regression method of estimation in survey sampling. Journal of Statistical Research, 35(2), pp. 35–44.

Singh, R. S., Sharma, P., (2015). Method of Estimation in the Presence of Non-response and Measurement Errors Simultaneously. Journal of Modern Applied Statistical Methods, 14(1), pp. 107-121. DOI: 10.22237/jmasm/1430453460.

Singh, P., Singh, R., Bouza, C. N., (2018). Effect of measurement error and non-response on estimation of population mean. Revista Investigacion Operacional, 39(1), pp. 108– 120.

Searls, D. T., (1964). The Utilization of a Known Coefficient of Variation in the Estimation Procedure. Journal of the American Statistical Association, 59, pp. 1225–1226.

Srivastava, S. K., (1967). An estimator using auxiliary information in sample surveys, Calcutta Statistical Association Bulletin, 16, pp. 121-–132.

Singh, H. P., Espejo, M. R., (2003). On Linear Regression and Ratio-product Estimation of a Finite Population Mean. The StatistiSingh, H. P. and Espejo, M. R.cian, 52(1), pp. 59–67.

Tiwari, K. K., Bhougal, S., Kumar, S., Rather, K. U. I., (2022). Using Randomized Response to Estimate the Population Mean of a Sensitive Variable under the Influence of Measurement Error. Journal of Statistical Theory and Practice, 16(2), pp. 1-11. https://doi.org/10.1007/s42519-022-00251-1.

Tiwari, K. K., Bhougal, S., Kumar, S., Onyango, R., (2022). Assessing the Effect of Nonresponse and Measurement Error Using a Novel Class of Efficient Estimators. Journal of Mathematics, Article ID 4946265. DOI: 10.1155/2022/4946265.

Tiwari, K. K., Bhougal, S., Kumar, S., (2023). A General Class of Estimators in the Presence of Non-response and Measurement Error, Journal of Statistics Application & Probability Letters, 10(1), pp. 13-33. http://dx.doi.org/10.18576/jsapl/100102.

Zahid, E., Shabbir, J., Gupta, S., Onyango, R., Saeed, S., (2022). A generalized class of estimators for sensitive variable in the presence of measurement error and non-response. PLoS ONE 17(1), e0261561. https://doi.org/10.1371/journal. Pone.0261561.