New memory-based ratio estimator in survey sampling

Authors

  • Irfan Aslam Department of Statistics, Government Islamia Graduate College, Lahore, Punjab, Pakistan. https://orcid.org/0009-0006-0007-6453
  • Muhammad Noorul Amin Department of Statistics, COMSATS University Islamabad, Lahore Campus, Lahore, Punjab, Pakistan. https://orcid.org/0000-0003-2882-221X
  • Amjad Mahmood Punjab College of Information Technology, Lahore, Punjab, Pakistan | Hailey College of Commerce, University of the Punjab, Lahore, Punjab, Pakistan. https://orcid.org/0009-0006-6396-2305
  • Prayas Sharma Department of Statistics, Babasaheb Bhimrao Ambedkar University, Lucknow, India.

DOI:

https://doi.org/10.47264/idea.nasij/5.1.11

Keywords:

Auxiliary information, Ratio estimator, Smoothing constant, Mean square, Relative efficiency, Simple random sampling, Memory type estimate, New estimator, Simulation

Abstract

This study proposes a new estimator based on the Exponential Weighted Moving Average (EWMA) statistic by following the concept of Noor-ul-Amin (2021). The EWMA model consumed contemporary and empirical data to enhance the competence of the population mean estimation. The memory type estimate is proposed with a twofold utilisation of Auxiliary Information (AUI) in alignment with the sampling type, i.e., Simple Random Sampling (SRS). A detailed numerical study and analysis are conducted to estimate the projected efficiency. This study provides an efficient estimator for population mean in the occurrence of time series data. The extra advantage of using EWMA statistics instead of classical statistics is that we can get better effectiveness of the mean estimate of the population under SRS by altering the significance of the smooth constant ?, as the cost of the smoothing constant ? decreases from one towards zero, and we gain the efficiency of the suggested estimator. For ? = 1, the proposed estimator performs the same as their comparative estimator. This expands incompetence over the presented ones statistically demonstrated in mean square error and relative effectiveness. Previous research is also accessed with everyday life information that indicates the conclusions of the simulation investigation.

References

Aslam, I., Noor-ul-Amin, M., Yasmeen, U., & Hanif, M. (2020). Memory type ratio and product estimators in stratified sampling. Journal of Reliability and Statistical Studies, 13(01), 1–20. https://doi.org/10.13052/jrss0974-8024.1311 DOI: https://doi.org/10.13052/jrss0974-8024.1311

Aslam, I., Noor-ul-Amin, M., Hanif, M., & Sharma, P. (2023). Memory type ratio and product estimators under ranked-based sampling schemes. Communications in Statistics-Theory and Methods, 52(4), 1155–1177. https://doi.org/10.1080/03610926.2021.1924784 DOI: https://doi.org/10.1080/03610926.2021.1924784

Bahl, S., & Nain, M. (1999). Difference-cum-ratio type estimators. Journal of Statistics and Management Systems, 2(1), 1–8. https://doi.org/10.1080/09720510.1999.10700986

Bhushan, S., Kumar, A., Al-Omari, A. I., & Alomani, G. A. (2023). Mean estimation for time-based surveys using memory-type logarithmic estimators. Mathematics, 11(9), 2125. https://doi.org/10.3390/math11092125 DOI: https://doi.org/10.3390/math11092125

Cochran, W. (1940). The estimation of the yields of cereal experiments by sampling for the ratio of grain to total produce. The Journal of Agricultureal Science, 30(2), 262–275. https://doi.org/10.1017/S0021859600048012 DOI: https://doi.org/10.1017/S0021859600048012

Chhaparwal, P., & Kumar, S. (2022). Improving efficiencies of ratio-and product-type estimators for estimating population mean for time-based survey. Journal of Reliability and Statistical Studies, 325–340. DOI: https://doi.org/10.13052/jrss0974-8024.15113

Javaid, A., Noor-ul-Amin, M., & Hanif, M. (2019). Modified ratio estimator in systematic random sampling under non-response. Proceedings of the National Academy of Sciences, India Section A: Physical Sciences, 89, 817–825. https://doi.org/10.1007/s40010-018-0509-3 DOI: https://doi.org/10.1007/s40010-018-0509-3

Jhajj, H. S., & Walia, G. S. (2012). A generalized difference-cum-ratio type estimator for the population mean in double sampling. Communications in Statistics: Simulation and Computation, 41(1), 58–64. https://doi.org/10.1080/03610918.2011.579366 DOI: https://doi.org/10.1080/03610918.2011.579366

Kadilar, C., Candan, M., & Cingi, H. (2007). Ratio estimators using robust regression. Hacettepe Journal of Mathematics and Statistics, 36(2), 181–188.

Kadilar, C., & Cingi, H. (2004). Ratio estimators in simple random sampling. Applied Mathematics and Computation, 151(3), 893–902. https://doi.org/10.1016/S0096-3003(03)00803-8 DOI: https://doi.org/10.1016/S0096-3003(03)00803-8

Kadilar, G. Ö. (2016). A new exponential type estimator for the population mean in simple random sampling. Journal of Modern Applied Statistical Methods, 15(2), 207–214. https://doi.org/10.56801/10.56801/v15.i.848 DOI: https://doi.org/10.22237/jmasm/1478002380

Kumar, S., & Chhaparwal, P. (2019). Ratio- and product-based estimators using known coefficient of variation of the auxiliary variable via modified maximum likelihood. Life Cycle Reliability and Safety Engineering, 8(2), 99–116. https://doi.org/10.1007/s41872-019-00077-0 DOI: https://doi.org/10.1007/s41872-019-00077-0

Noor-ul-Amin, M. (2021). Memory type estimators of population mean using exponentially weighted moving averages for time scaled surveys. Communications in Statistics - Theory and Methods, 50(12), 2747–2758. https://doi.org/10.1080/03610926.2019.1670850 DOI: https://doi.org/10.1080/03610926.2019.1670850

Qureshi, M. N, Tariq, M. U, & Hanif M. (2022). Memory-type ratio and product estimators for population variance using exponentially weighted moving averages for time-scaled surveys. Communications in Statistics - Simulation and Computation, 53(3), 1484–1493. https://doi.org/10.1080/03610918.2022.2050390 DOI: https://doi.org/10.1080/03610918.2022.2050390

Ray, S. K., & Singh, R. K. (1981). Difference-cum-ratio type estimators. Journal - Indian Statistical Association, 19, 147–151. https://doi.org/10.1080/09720510.1999.10700986 DOI: https://doi.org/10.1080/09720510.1999.10700986

Roberts, S. W. (1959). Control Chart Tests Based on Geometric Moving Averages. Technometrics, 1(3), 239–250. https://doi.org/10.1080/00401706.1959.10489860 DOI: https://doi.org/10.1080/00401706.1959.10489860

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(1), 199. https://doi.org/10.15446/rce.v37n1.44366 DOI: https://doi.org/10.15446/rce.v37n1.44366

Sisodia, B. and Dwivedi, V. (1981) Modified Ratio Estimator Using Coefficient of Variation of Auxiliary Variable. Journal-Indian Society of Agricultural Statistics, 33, 13-18. https://www.scirp.org/reference/referencespapers?referenceid=2166269

Upadhyaya, L. N., & Singh, H. P. (1999). Use of transformed auxiliary variable in estimating the finite population mean. Biometrical Journal, 41(5), 627–636. https://doi.org/10.1002/(SICI)1521-4036(199909)41 DOI: https://doi.org/10.1002/(SICI)1521-4036(199909)41:5<627::AID-BIMJ627>3.3.CO;2-N

Zahid, R., Noor-ul-Amin, M., Khan, I., AlQahtani, S. A., Pathak, P. K., & Rahimi, J. (2023). Combination of memory type ratio and product estimators under extended EWMA statistic with application to wheat production. Scientific Reports, 13(1), 13547. https://www.nature.com/articles/s41598-023-40687-4 DOI: https://doi.org/10.1038/s41598-023-40687-4

Published

2024-06-28

How to Cite

Aslam, I., Amin, M. N., Mahmood, A., & Sharma, P. (2024). New memory-based ratio estimator in survey sampling. Natural and Applied Sciences International Journal (NASIJ), 5(1), 168–181. https://doi.org/10.47264/idea.nasij/5.1.11

Issue

Section

Research Articles