Ratio estimation of two population means in two-phase stratified random sampling under a scrambled response situation

• Authors: Pitambar Das , Garib Nath Singh , Arnab Bandyopadhyay

Abstracts

EN

In this paper, we have described the development of an effective two-phase stratified random sampling estimation procedure in a scrambled response situation. Two different exponential, regression-type estimators were formed separately for different structures of two-phase stratified sampling schemes. We have studied the properties of the suggested strategy. The performance of the proposed strategy has been demonstrated through numerical evidence based on a data set of a natural population and a population generated through simulation studies. Taking into consideration the encouraging findings, suitable recommendations for survey statisticians are prepared for the application of the proposed strategy in real-life conditions.

Keywords

EN

stratified random sampling; scrambled response; auxiliary variable; mean square error; simulation study

• Publisher: Główny Urząd Statystyczny
• Journal: Statistics in Transition new series
• Year: 2023
• Volume: 24
• Issue: 5
• Pages: 45-61

Dates

published

2023

Contributors

author

Pitambar Das

• Department of Mathematics, Netaji Nagar Day College

author

Garib Nath Singh

• Department of Mathematics & Computing, Indian Institute of Technology (Indian School of Mines)

author

Arnab Bandyopadhyay

• Department of Mathematics, Asansol Engineering College

• https://orcid.org/0000000207697491

References

• Diana, G., Perri, P. F., (2010). New scrambled response models for estimating the mean of a sensitive quantitative character. Journal of Applied Statistics, Vol. 37, pp. 1875- 1890.
• Eichhorn, B., Hayre, L. S., (1983). Scrambled randomized response methods for obtaining sensitive quantitative data. Journal of Statistical Planning and Inference, Vol. 7, pp. 307-316.
• Giancarlo, D., Pier, P. F., (2010). New scrambled response models for estimating the mean of a sensitive quantitative character. Journal of Applied Statistics, Vol. 37, pp.1875-1890, DOI: 10.1080/02664760903186031.
• Greenberg, B. G., Kuebler, R. R., Abernathy, J. R., Horvitz, D. G., (1971). Application of the randomized response technique in obtaining quantitative data. Journal of American Statistical Association, Vol. 66, pp. 243-250.
• Kadilar, C., Cingi, H., (2000). Ratio Estimator in stratified sampling. Biometrical Journal, Vol. 45, pp. 218-225.
• Kadilar, C., Cingi, H., (2003). A new ratio Estimator in stratified sampling. Communication in Statistics-Theory and Methods, Vol. 34, pp. 597-602.
• Pollock, K. H., Bek, Y., (1976). A comparison of three randomized response models for quantitative data. Journal of American Statistical Association, Vol. 71, pp. 884-886.
• Koyuncu, N., Kadilar, C., (2008). Ratio and product estimators in stratified random sampling. Journal of Statistical Planning and Inference, Vol. 139, pp. 2552-2558.
• Koyuncu, N., Kadilar, C., (2009). Family of estimators of population mean using two auxiliary variables in stratified random sampling. Communications in StatisticsTheory and Methods, Vol. 38, pp. 2398-2417.
• Reddy, V.N., (1978). A study on the use of prior knowledge on certain population parameters in estimation. Sankhya, Series C, 40, pp. 29-37.
• Shabbir, J., Gupta, S., (2005). Improved ratio estimators in stratified sampling. American Journal of Mathematical and Management Sciences, Vol. 25, pp. 293-311.
• Singh, S., Deo, B., (2003). Imputation by power transformation. Statistical Papers, Vol. 4, pp. 555-579.
• Singh, H.P., Vishwakarma, G. K., (2005). Combined Ratio - product Estimator of Finite Population Mean in Stratified Sampling. Metodologia de Encuestas, Vol. 8, pp. 35- 44.
• Singh, R., Sukhatme, B. V., (1973). Optimum stratification with ratio and regression method of estimation. Annals of the Institute of Statistical Mathematics, Vol. 25, pp. 627-633.
• Singh, R., Kumar, M., Chaudhary, M. K., Kadilar, C., (2009). Improved Exponential estimator in Stratified Random Sampling. Pakistan Journal of Statistics and Operation Research, Vol. 5, pp. 67-82.
• Singh, H. P., Chandra, P., Joarder, A. H., Singh, S., (2007). Family of estimators of mean, ratio and product of a finite population using random non-response. Test, Vol. 16, pp. 565-597.
• Singh, G. N., Sharma, A. K., Bandyopadhyay, A., (2017). Effectual Variance Estimation Strategy in Two Occasions Successive Sampling in Presence of Random NonResponse. Communications in Statistics-Theory & Methods, Vol. 46, pp. 7201-7224.
• Tracy, D. S., Singh, H. P., Singh, R., (1996). An alternative to the ratio-cum-product estimator in sample surveys. Journal of Statistical Planning and Inference, Vol. 53, pp. 375-387.

Identifiers

DOI

10.59170/stattrans-2023-063

Biblioteka Nauki

31342165