Published

2025-01-01

A Class of Ratio Cum Product Estimators with Non-Response and Measurement Error Using ORRT Models: A Double Sampling Scheme

Una clase de estimadores de relación con producto con falta de respuesta y error de medición utilizando modelos ORRT: un esquema de muestreo doble

DOI:

https://doi.org/10.15446/rce.v48n1.118163

Keywords:

Sensitive variable, Non-response, Measurement error, Double sampling, Optional Randomized Response Technique (ORRT) (en)
Variable sensible, Falta de respuesta, Error de medición, Doble muestreo, Técnica de Respuesta Aleatoria Opcional (ORRT) (es)

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Authors

  • Sunil Kumar University of Jammu
  • Sanam Preet Kour Sharda University
  • Housila P. Singh Vikram University Ujjain

The current study employs the ratio-cum-product estimator to estimate the population mean of a sensitive study variable, aiming to overcome issues related to non-response and measurement error in the context of double sampling. The characteristics of the proposed class of estimators are computed up to the first order of approximation. A comparative analysis is conducted to assess the performance of the suggested estimator amongst the class of estimator and the estimator proposed by Kumar & Zhang (2023). Additionally, theoretical findings are supported by conducting two model-based simulation study by using a hypothetical population. The simulation results demonstrate that the proposed ratio-cum-product estimator under double sampling exhibits the lowest mean squared error among Kumar & Zhang (2023) estimator and all classes of suggested estimator which indicates their superior performance in estimating the population mean of a sensitive variable. As a result, the suggested estimator offers a valuable tool for estimating the population mean in surveys conducted across various agriculture, environmental studies, market research and health surveys.

El presente estudio emplea el estimador de razón-producto para estimar la media poblacional de una variable de estudio sensible, con el objetivo de superar los problemas relacionados con la falta de respuesta y el error de medición en el contexto del muestreo doble. Las características de la clase de estimadores propuesta se calculan hasta el primer orden de aproximación. Se realiza un análisis comparativo para evaluar el desempeño del estimador sugerido entre la clase de estimador y el estimador propuesto por Kumar & Zhang (2023). Además, los hallazgos teóricos se respaldan mediante la realización de un estudio de simulación utilizando una población creada artificialmente. Los resultados de la simulación demuestran que el estimador de razón-producto propuesto bajo muestreo doble exhibe el error cuadrático medio más bajo entre el estimador de Kumar & Zhang (2023) y todas las clases de estimador sugerido, lo que indica su desempeño superior en la estimación de la población. media de una variable sensible. Como resultado, el estimador sugerido ofrece una herramienta valiosa para estimar la media poblacional en encuestas realizadas en diversos estudios agrícolas, ambientales, de mercado y de salud.

References

Azeem, M., S. N. H. S. I. M. & Salam, A. (2024), `An efficient estimator of population variance of a sensitive variable with a new randomized response technique', Heliyon 10(5), 1-11.

Dash, P. and Sunani, K. (2022), `An improved class of mixed estimators of population mean under double sampling', Indian Journal of Science and Technology 15(7), 276-291.

Diana, G. and Perri, P. F. (2011), `A class of estimators for quantitative sensitive data, statistical papers', Statistical Papers 52, 633-650.

Eichhorn, B. H. and Hayre, L. S. (1983), `Scrambled randomized response methods for obtaining sensitive quantitative data', Journal of Statistical Planning and Inference 7(4), 307-316.

Gupta, S., Gupta, B. and Singh, S. (2002), `Estimation of sensitivity level of personal interview survey questions', Journal of Statistical Planning and inference 100, 239-247.

Gupta, S. N. and Thornton, B. and Shabbir, J. and Singhal, S. (2006), `A comparison of multiplicative and additive optional rrt models', Journal of Statistical Theory and Applications 5(3), 226-239.

Hansen, M. H. and Hurwitz, W. N. (1946), `The problem of non-response in sample surveys', Journal of the American Statistical Association 41(236), 517-529.

Kumar, S. and Kour, S. P. (2021), `Estimation of sensitive variable in two-phase sampling under measurement error and non-response using ORRT models', Sri Lankan Journal of Applied Statistics 22, 95-122.

Kumar, S., K. S. G. R. & Joorel, J. P. S. (2023), `A class of logarithmic type estimator under non-response and measurement error using ORRT models', Journal of the Indian Society for Probability and Statistics 24(2), 333-356.

Kumar, S., K. S. P. & Zhang, Q. (2023), `An enhanced ratio-cum-product estimator with non-response and observational error by utilizing ORRT models: a sensitive estimation approach', Journal of Statistical Computation and Simulation 93(5), 818-836.

Kumar, S. & Kour, S. P. (2022), `The joint influence of estimation of sensitive variable under measurement error and non-response using ORRT models', Journal of Statistical Computation and Simulation 92(17), 3583-3604.

Neyman, J. (1934), `On two different aspects of the representative method: The method of stratified sampling and the method of purposive selection', Journal of the Royal Statistical Society 97(4), 558-606.

Pradhan, B. (2014), `Three phase stratified sampling with ratio method of estimation', Statistical 73(2), 235-251.

Saha, A. (2008), `A randomized response technique for quantitative data under unequal probability sampling', Journal of Statistical Theory and Practice 2(4), 589-596.

Shabbir, J. and Ahmed, S. and Sanaullah, A. and Onyango, R. (2021), `Measuring performance of ratio-exponential-log type general class of estimators using two auxiliary variables', Mathematical Problems in Engineering 2021(18), 1-12.

Singh, B. and Choudhury, S. (2012), `Exponential chain ratio and product type estimators for population mean under double sampling technique', Journal of Science Frontier Research in Mathematics and Design Sciences 12(6), 13-23.

Warner, S. L. (1965), `Randomized response: a survey technique for eliminating evasive answer bias', Journal of the American Statistical Association 60(309), 63-69.

Zaman, T. and Kadilar, C. (2019), `New class of exponential estimators for finite population mean in two-phase sampling', Communications in Statistics-Theory and Methods 50, 1-16.

Zhang, Q., Khalil, S. and Gupta, S. (2021), `Mean estimation of sensitive variables under non-response and measurement errors using optional RRT models', Journal of Statistical Theory and Practice 15(3).

How to Cite

APA

Kumar, S., Kour, S. P. and Singh, H. P. (2025). A Class of Ratio Cum Product Estimators with Non-Response and Measurement Error Using ORRT Models: A Double Sampling Scheme. Revista Colombiana de Estadística, 48(1), 215–237. https://doi.org/10.15446/rce.v48n1.118163

ACM

[1]
Kumar, S., Kour, S.P. and Singh, H.P. 2025. A Class of Ratio Cum Product Estimators with Non-Response and Measurement Error Using ORRT Models: A Double Sampling Scheme. Revista Colombiana de Estadística. 48, 1 (Jan. 2025), 215–237. DOI:https://doi.org/10.15446/rce.v48n1.118163.

ACS

(1)
Kumar, S.; Kour, S. P.; Singh, H. P. A Class of Ratio Cum Product Estimators with Non-Response and Measurement Error Using ORRT Models: A Double Sampling Scheme. Rev. colomb. estad. 2025, 48, 215-237.

ABNT

KUMAR, S.; KOUR, S. P.; SINGH, H. P. A Class of Ratio Cum Product Estimators with Non-Response and Measurement Error Using ORRT Models: A Double Sampling Scheme. Revista Colombiana de Estadística, [S. l.], v. 48, n. 1, p. 215–237, 2025. DOI: 10.15446/rce.v48n1.118163. Disponível em: https://revistas.unal.edu.co/index.php/estad/article/view/118163. Acesso em: 19 feb. 2025.

Chicago

Kumar, Sunil, Sanam Preet Kour, and Housila P. Singh. 2025. “A Class of Ratio Cum Product Estimators with Non-Response and Measurement Error Using ORRT Models: A Double Sampling Scheme”. Revista Colombiana De Estadística 48 (1):215-37. https://doi.org/10.15446/rce.v48n1.118163.

Harvard

Kumar, S., Kour, S. P. and Singh, H. P. (2025) “A Class of Ratio Cum Product Estimators with Non-Response and Measurement Error Using ORRT Models: A Double Sampling Scheme”, Revista Colombiana de Estadística, 48(1), pp. 215–237. doi: 10.15446/rce.v48n1.118163.

IEEE

[1]
S. Kumar, S. P. Kour, and H. P. Singh, “A Class of Ratio Cum Product Estimators with Non-Response and Measurement Error Using ORRT Models: A Double Sampling Scheme”, Rev. colomb. estad., vol. 48, no. 1, pp. 215–237, Jan. 2025.

MLA

Kumar, S., S. P. Kour, and H. P. Singh. “A Class of Ratio Cum Product Estimators with Non-Response and Measurement Error Using ORRT Models: A Double Sampling Scheme”. Revista Colombiana de Estadística, vol. 48, no. 1, Jan. 2025, pp. 215-37, doi:10.15446/rce.v48n1.118163.

Turabian

Kumar, Sunil, Sanam Preet Kour, and Housila P. Singh. “A Class of Ratio Cum Product Estimators with Non-Response and Measurement Error Using ORRT Models: A Double Sampling Scheme”. Revista Colombiana de Estadística 48, no. 1 (January 21, 2025): 215–237. Accessed February 19, 2025. https://revistas.unal.edu.co/index.php/estad/article/view/118163.

Vancouver

1.
Kumar S, Kour SP, Singh HP. A Class of Ratio Cum Product Estimators with Non-Response and Measurement Error Using ORRT Models: A Double Sampling Scheme. Rev. colomb. estad. [Internet]. 2025 Jan. 21 [cited 2025 Feb. 19];48(1):215-37. Available from: https://revistas.unal.edu.co/index.php/estad/article/view/118163

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