Regression-in-Ratio Estimators for Population Mean by Using Robust Regression in Two Phase Sampling
The estimation of population mean is not meaningful using ordinary least square method when data contains some outliers. In the current study, we proposed efficient estimators of population mean using robust regression in two phase sampling. An extensive simulation study is conduct to examine the efficiency of proposed estimators in terms of mean square error (MSE). Real life example and extensive simulation study are cited to demonstrate the performance of the proposed estimators. Theoretical example and simulation studies showed that the suggested estimators are more efficient than the considered estimators in the presence of outliers.
Ahuja, T.K., Misra, P. and Behwal, O.K. (2021). A generalized two phase sampling estimator of ratio of population means using Auxilary information. Journal of Reliability and Statistical Studies, 14(1), pp. 1–16.
Anas, M.M., Huang, Z., Alilah, D.A. Shafqat, M. and Hussain, S. (2021). Mean estimators using robust quantile regression and L-moments’ characteristics for complete and partial auxiliary information. Mathematical Problems in Engineering, 1, pp. 1–8.
Chand, L. (1975). Some Ratio-Type Estimator Based on Two or More Auxiliary Variables. Unpublished Ph.D. dissertation). Iowa State University, Iowa.
Davison, A.C. and Hinkley, D.V. (1997). Bootstrap Methods and Their Application. Cambridge University Press. https://doi.org/10.1155/2021/9242895
Huber, P.J. (1964). Robust estimation of a location parameter. The Annals of Mathematical Statistics, 35(1), pp. 73–101.
Kadilar, C. and Cingi, H. (2004). Ratio estimators in simple random sampling. Applied Mathematics and Computation, 151, pp. 893–902.
Kiregyera, B. (1984). Regression-type estimators using two auxiliary variables and model of two phase sampling from finite populations. Metrika, 31, pp. 215–226.
Menezes, D.Q.F., Prata, D.M., Secchi, A. R. and Pinto, J. C. (2021). A review on robust M-estimator for regression analysis. Commuters & Chemical Engineering, 147. https://doi.org/10.1016/j.compchemeng.2021.107254
Misra, P. (2018). Regression type double sampling estimator of population mean using auxiliary information. Journal of Reliability and Statistical Studies, 11(1), pp. 21–28.
Neyman, J. (1938). Contribution to the theory of sampling human populations. Journal of American Statistical Association, 33, pp. 101–116.
Noor-ul-Amin, M., Shahbaz, Q.M. and Kadilar, C. (2016). Ratio estimators of population mean using robust regression in two phase sampling. Gazi University Journal of Science, 29(4), pp. 793–798.
Raza, A., Noor-ul-Amin, M. and Hanif, M. (2019). Regression-in-ratio estimators in the presence of outliers based on redescending M-estimator. Journal of Reliability and Statistical Studies, 12(2), pp. 1–10.
Singh, H.P. and Vishwakarma, G.K. (2007). Modified exponential ratio and product estimators for finite population mean in two phase sampling. Austrian Journal of Statistics, 36(3), pp. 217–225.
Subzar, M., Al-Omari, A.I. and Alanzi, R.A. (2020). The robust regression methods for estimating of finite population mean based on SRSWOR in case of outliers. Computers, Materials and Continua, 65(1), pp. 125–138.
Vishwakarma, G.K. and Gangele, R.K. (2014). A class of chain ratio-type exponential estimators in two phase sampling using two auxiliary variates. Applied Mathematics and computation, 227, pp. 171–175.