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

Pitambar Das; Garib Nath Singh; Arnab Bandyopadhyay

doi:https://doi.org/10.59170/stattrans-2023-063

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

Pitambar Das Department of Mathematics, Netaji Nagar Day College, Kolkata- 700092, India , Garib Nath Singh Department of Mathematics & Computing, Indian Institute of Technology (Indian School of Mines), Dhanbad-826004, India , Arnab Bandyopadhyay Department of Mathematics, Asansol Engineering College, Asansol–713305, India ORCID:https://orcid.org/0000-0002-0769-7491 Statistics in Transition new series, vol. 24, 2023, 5, pages: 45-61 Published online: 7 December 2023 https://doi.org/10.59170/stattrans-2023-063

219 Views 22 Downloads

ARTICLE

(English) PDF

ABSTRACT

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

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

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 Statistics- Theory 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 Non- Response. 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.