Research Article
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Year 2023, Volume: 6 Issue: 4, 196 - 210, 25.12.2023
https://doi.org/10.33434/cams.1365151

Abstract

References

  • [1] S. L. Warner, Randomized response: a survey technique for eliminating evasive answer bias, J. Am. Stat. Assoc., 60(309) (1965), 63–69.
  • [2] B. G. Greenberg, R. R. Jr. Kuebler, J. R. Abernathy, D. G. Hovertiz, Application of the randomized response techniques in obtaining quantitative data, J. Am. Stat. Assoc., 66(334) (1971), 243-250.
  • [3] K. Pollock, Y. Bek, A comparison of three randomized response models for quantitative data, J. Am. Stat. Assoc., 71(356) (1976), 884-886.
  • [4] S. Gupta, B. Gupta, S. Singh, Estimation of sensitivity level of personal interview survey questions, J. Stat. Plan. Inference, 100(2) (2002), 239-247.
  • [5] S. Gupta, J. Shabbir, S. J. Sehra, Mean and sensitivity estimation in optional randomized response models, J. Stat. Plan. Inference, 140(10) (2010), 2870-2874.
  • [6] S. Gupta, J. Shabbir, R. Sousa, P. Corte-Real, Estimation of the mean of a sensitive variable in the presence of auxiliary information, Commun. Stat. Theory Methods, 41(13-14) (2012), 13-14.
  • [7] Q. Zhang, G. Kalucha, S. Gupta, S. Khalil, Ratio estimation of the mean under RRT models, Int. J. Stat. Manag. Syst., 22(1) (2018), 97-113.
  • [8] S. Kumar, S. P. Kour, Estimation of Sensitive Variable in Two-Phase Sampling under Measurement Error And Non-Response Using ORRT Models, Sri Lankan J. Appl. Stat., 22(3) (2021), 95-122.
  • [9] S. Kumar, S. P. Kour, The joint influence of estimation of sensitive variable under measurement error and non-response using ORRT models, J. Stat. Comput. Simul., 92(17) (2022), 3583-3604.
  • [10] S. Kumar, S. P. Kour, Q. Zhang An enhanced ratio-cum-product estimator with non-response and observational error by utilizing ORRT models: a sensitive estimation approach, J. Stat. Comput. Simul., 93(5) (2023), 818-836.
  • [11] S. Kumar, S. P. Kour, R. Gupta, J. P. S. Joorel A Class of Logarithmic Type Estimator Under Non-Response and Measurement Error Using ORRT Models, J. Indian Soc. Probab. Stat., (2023), doi:10.1007/s41096-023-00156-7.
  • [12] Q. Zaman, M. Ijaz, T. Zaman, A randomization tool for obtaining efficient estimators through focus group discussion in sensitive surveys, Commun. Stat. - Theory Methods, 52(10) (2023), 3414-3428.
  • [13] J. Neyman, Contribution to the theory of sampling human populations, J Am Stat Assoc., 33(201) (1938), 101-116.
  • [14] A. Sanaullah, H. Ali, M. Noor-ul-Amin, M. Hanif, Generalized exponential chain ratio estimators under stratified two-phase random sampling, Appl. Math. Comput., 226 (2014), 541-547.
  • [15] T. Zaman, C. Kadilar, New class of exponential estimators for finite population mean in two-phase sampling, Commun. Stat. Theory Methods, 50(4) (2021), 874-889.
  • [16] S. Khalil, Q. Zhang, S. Gupta, An enhanced two-phase sampling ratio estimator for estimating population mean, J. Sci. Res. 65(3) (2021), 1-16.
  • [17] S. Khalil, Q. Zhang, S. Gupta, Mean estimation of sensitive variables under measurement errors using optional RRT models, Commun. Stat. Simul. Comput., 50(5) (2021), 1417-1426.
  • [18] R. Onyango, B. Oduor, F. Odundol, Joint influence of measurement errors and randomized response technique on mean estimation under stratified double sampling, Open J. Math. Sci., 5(1) (2021), 192-199.
  • [19] M. H. Hansen, W. N. Hurwitz, The problem of non-response in sample surveys, J. Am. Stat. Assoc., 41(236) (1946), 517-529.
  • [20] G. Diana, S. Riaz, J. Shabbir, Hansen and Hurwitz estimator with scrambled response on the second call, J. Appl. Stat., 41(3) (2014), 596-611.
  • [21] S. Gupta, S. Mehta, J. Shabbir, S. Khalil, A unified measure of respondent privacy and model efficiency in quantitative RRT models, J. Stat. Theory Pract., 12(3) (2018), 506-511.
  • [22] Q. Zhang, S. Khalil, S. Gupta, Ratio estimation of the mean under RRT models, J. Stat. Theory Pract., 15(3) (2021), 97-113.
  • [23] P. Mukhopadhyay, G. N. Singh, A. Bandyopadhyay, A general estimation technique of population mean under stratified successive sampling in presence of random scrambled response and non-response, Commun. Stat. Simul. Comput, 50(5) (2021), 1417-1426.
  • [24] G. Diana, P. F. Perri, A class of estimators for quantitative sensitive data, Stat. Pap., 52(3) (2011), 633-650.
  • [25] S. Khalil, M. Amin, M. Hanif, Estimation of population mean for a sensitive variable in the presence of measurement error, Int. J. Stat. Manag. Syst., 21(1) (2018), 81-91.
  • [26] Z. Yan, J.Wang, J. Lai, An efficiency and protection degree-based comparison among the quantitative randomized response strategies, Commun. Stat. - Theory Methods, 38(3) (2008), 400-408.

Quantify the Impact of Non-Response and Measurement Error of Sensitive Variable(s) under Two-Phase Sampling employing ORRT Models

Year 2023, Volume: 6 Issue: 4, 196 - 210, 25.12.2023
https://doi.org/10.33434/cams.1365151

Abstract

Throughout this article, a two-phase sampling (TPS) technique is employed to estimate the population mean of the sensitive variable. The current article endeavours to develop a chain ratio type estimator for the estimation of sensitive variable(s) in the presence of non-response and measurement error simultaneously by utilizing ORRT models under a two-phase sampling technique. The significant aspects associated with the suggested estimator characterized by bias and mean squared error have been evaluated. Besides this, the utterance for the minimum mean squared error for the optimal values has also been identified. The supremacy of the proposed estimator has been compared with the modified existing estimators under the TPS scheme by using two sensitive auxiliary variables. To clarify the theoretical findings, a simulation study along with a hypothetical generated population and a real population which is based on abortion rates from Statistical Abstract of the United States: 2011 are also addressed in this study.

References

  • [1] S. L. Warner, Randomized response: a survey technique for eliminating evasive answer bias, J. Am. Stat. Assoc., 60(309) (1965), 63–69.
  • [2] B. G. Greenberg, R. R. Jr. Kuebler, J. R. Abernathy, D. G. Hovertiz, Application of the randomized response techniques in obtaining quantitative data, J. Am. Stat. Assoc., 66(334) (1971), 243-250.
  • [3] K. Pollock, Y. Bek, A comparison of three randomized response models for quantitative data, J. Am. Stat. Assoc., 71(356) (1976), 884-886.
  • [4] S. Gupta, B. Gupta, S. Singh, Estimation of sensitivity level of personal interview survey questions, J. Stat. Plan. Inference, 100(2) (2002), 239-247.
  • [5] S. Gupta, J. Shabbir, S. J. Sehra, Mean and sensitivity estimation in optional randomized response models, J. Stat. Plan. Inference, 140(10) (2010), 2870-2874.
  • [6] S. Gupta, J. Shabbir, R. Sousa, P. Corte-Real, Estimation of the mean of a sensitive variable in the presence of auxiliary information, Commun. Stat. Theory Methods, 41(13-14) (2012), 13-14.
  • [7] Q. Zhang, G. Kalucha, S. Gupta, S. Khalil, Ratio estimation of the mean under RRT models, Int. J. Stat. Manag. Syst., 22(1) (2018), 97-113.
  • [8] S. Kumar, S. P. Kour, Estimation of Sensitive Variable in Two-Phase Sampling under Measurement Error And Non-Response Using ORRT Models, Sri Lankan J. Appl. Stat., 22(3) (2021), 95-122.
  • [9] S. Kumar, S. P. Kour, The joint influence of estimation of sensitive variable under measurement error and non-response using ORRT models, J. Stat. Comput. Simul., 92(17) (2022), 3583-3604.
  • [10] S. Kumar, S. P. Kour, Q. Zhang An enhanced ratio-cum-product estimator with non-response and observational error by utilizing ORRT models: a sensitive estimation approach, J. Stat. Comput. Simul., 93(5) (2023), 818-836.
  • [11] S. Kumar, S. P. Kour, R. Gupta, J. P. S. Joorel A Class of Logarithmic Type Estimator Under Non-Response and Measurement Error Using ORRT Models, J. Indian Soc. Probab. Stat., (2023), doi:10.1007/s41096-023-00156-7.
  • [12] Q. Zaman, M. Ijaz, T. Zaman, A randomization tool for obtaining efficient estimators through focus group discussion in sensitive surveys, Commun. Stat. - Theory Methods, 52(10) (2023), 3414-3428.
  • [13] J. Neyman, Contribution to the theory of sampling human populations, J Am Stat Assoc., 33(201) (1938), 101-116.
  • [14] A. Sanaullah, H. Ali, M. Noor-ul-Amin, M. Hanif, Generalized exponential chain ratio estimators under stratified two-phase random sampling, Appl. Math. Comput., 226 (2014), 541-547.
  • [15] T. Zaman, C. Kadilar, New class of exponential estimators for finite population mean in two-phase sampling, Commun. Stat. Theory Methods, 50(4) (2021), 874-889.
  • [16] S. Khalil, Q. Zhang, S. Gupta, An enhanced two-phase sampling ratio estimator for estimating population mean, J. Sci. Res. 65(3) (2021), 1-16.
  • [17] S. Khalil, Q. Zhang, S. Gupta, Mean estimation of sensitive variables under measurement errors using optional RRT models, Commun. Stat. Simul. Comput., 50(5) (2021), 1417-1426.
  • [18] R. Onyango, B. Oduor, F. Odundol, Joint influence of measurement errors and randomized response technique on mean estimation under stratified double sampling, Open J. Math. Sci., 5(1) (2021), 192-199.
  • [19] M. H. Hansen, W. N. Hurwitz, The problem of non-response in sample surveys, J. Am. Stat. Assoc., 41(236) (1946), 517-529.
  • [20] G. Diana, S. Riaz, J. Shabbir, Hansen and Hurwitz estimator with scrambled response on the second call, J. Appl. Stat., 41(3) (2014), 596-611.
  • [21] S. Gupta, S. Mehta, J. Shabbir, S. Khalil, A unified measure of respondent privacy and model efficiency in quantitative RRT models, J. Stat. Theory Pract., 12(3) (2018), 506-511.
  • [22] Q. Zhang, S. Khalil, S. Gupta, Ratio estimation of the mean under RRT models, J. Stat. Theory Pract., 15(3) (2021), 97-113.
  • [23] P. Mukhopadhyay, G. N. Singh, A. Bandyopadhyay, A general estimation technique of population mean under stratified successive sampling in presence of random scrambled response and non-response, Commun. Stat. Simul. Comput, 50(5) (2021), 1417-1426.
  • [24] G. Diana, P. F. Perri, A class of estimators for quantitative sensitive data, Stat. Pap., 52(3) (2011), 633-650.
  • [25] S. Khalil, M. Amin, M. Hanif, Estimation of population mean for a sensitive variable in the presence of measurement error, Int. J. Stat. Manag. Syst., 21(1) (2018), 81-91.
  • [26] Z. Yan, J.Wang, J. Lai, An efficiency and protection degree-based comparison among the quantitative randomized response strategies, Commun. Stat. - Theory Methods, 38(3) (2008), 400-408.
There are 26 citations in total.

Details

Primary Language English
Subjects Statistics (Other)
Journal Section Articles
Authors

Sunil Kumar 0000-0003-0249-8415

Sanam Preet Kour 0000-0002-2894-2556

Early Pub Date December 5, 2023
Publication Date December 25, 2023
Submission Date September 23, 2023
Acceptance Date November 16, 2023
Published in Issue Year 2023 Volume: 6 Issue: 4

Cite

APA Kumar, S., & Kour, S. P. (2023). Quantify the Impact of Non-Response and Measurement Error of Sensitive Variable(s) under Two-Phase Sampling employing ORRT Models. Communications in Advanced Mathematical Sciences, 6(4), 196-210. https://doi.org/10.33434/cams.1365151
AMA Kumar S, Kour SP. Quantify the Impact of Non-Response and Measurement Error of Sensitive Variable(s) under Two-Phase Sampling employing ORRT Models. Communications in Advanced Mathematical Sciences. December 2023;6(4):196-210. doi:10.33434/cams.1365151
Chicago Kumar, Sunil, and Sanam Preet Kour. “Quantify the Impact of Non-Response and Measurement Error of Sensitive Variable(s) under Two-Phase Sampling Employing ORRT Models”. Communications in Advanced Mathematical Sciences 6, no. 4 (December 2023): 196-210. https://doi.org/10.33434/cams.1365151.
EndNote Kumar S, Kour SP (December 1, 2023) Quantify the Impact of Non-Response and Measurement Error of Sensitive Variable(s) under Two-Phase Sampling employing ORRT Models. Communications in Advanced Mathematical Sciences 6 4 196–210.
IEEE S. Kumar and S. P. Kour, “Quantify the Impact of Non-Response and Measurement Error of Sensitive Variable(s) under Two-Phase Sampling employing ORRT Models”, Communications in Advanced Mathematical Sciences, vol. 6, no. 4, pp. 196–210, 2023, doi: 10.33434/cams.1365151.
ISNAD Kumar, Sunil - Kour, Sanam Preet. “Quantify the Impact of Non-Response and Measurement Error of Sensitive Variable(s) under Two-Phase Sampling Employing ORRT Models”. Communications in Advanced Mathematical Sciences 6/4 (December 2023), 196-210. https://doi.org/10.33434/cams.1365151.
JAMA Kumar S, Kour SP. Quantify the Impact of Non-Response and Measurement Error of Sensitive Variable(s) under Two-Phase Sampling employing ORRT Models. Communications in Advanced Mathematical Sciences. 2023;6:196–210.
MLA Kumar, Sunil and Sanam Preet Kour. “Quantify the Impact of Non-Response and Measurement Error of Sensitive Variable(s) under Two-Phase Sampling Employing ORRT Models”. Communications in Advanced Mathematical Sciences, vol. 6, no. 4, 2023, pp. 196-10, doi:10.33434/cams.1365151.
Vancouver Kumar S, Kour SP. Quantify the Impact of Non-Response and Measurement Error of Sensitive Variable(s) under Two-Phase Sampling employing ORRT Models. Communications in Advanced Mathematical Sciences. 2023;6(4):196-210.

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