Main Article Content

Abstract

In this article, a class of Poisson-regression based estimators has been proposed for estimating the finite population mean in simple random sampling without replacement (SRSWOR). The Poisson-regression model is the most common method used to model count responses in many studies. The expression for bias and mean square error (MSE) of proposed class of estimators are obtained up to first order of approximation. The proposed estimators have been compared theoretically with the existing estimators, and the condition under which the proposed class of estimators perform better than existing estimators have been obtained. Two real data sets are considered to assess the performance of the proposed estimators. Numerical findings confirms that the proposed estimators dominate over the existing estimators such as Koc (2021) and Usman et al. (2021) in terms of mean squared error.

Keywords

Ratio estimator Poisson regression Mean Square error Bias Efficiency Auxiliary variable

Article Details

Author Biographies

S.E.H. Rizvi , Division of Statistics and Computer Science, Main Campus SKUAST-J, Chatha Jammu-180009, India

Proffessor in the Division of Statistics and Computer Science SKUAST jammu and currently Dean of the Basic Science also

 

Manish Sharma, Division of Statistics and Computer Science, Main Campus SKUAST-J, Chatha Jammu-180009, India

Proffessor and Head of the Division of Statistics and Computer Science

M. Iqbal Jeelani Bhat , Division of Statistics and Computer Science, Main Campus SKUAST-J, Chatha Jammu-180009, India

Assistant Proffessor Division of Statistics and Computer Science

Saqib Mushtaq, Department of Mathematics, Main Campus University of Kashmir Srinagar-190006-India

Research Scholar

How to Cite
Jana, Z. H. W., Rizvi , S., Sharma, M., Bhat , M. I. J., & Mushtaq, S. (2022). Modified Regression Estimators for Improving Mean Estimation -Poisson Regression Approach . Pakistan Journal of Statistics and Operation Research, 18(4), 985-994. https://doi.org/10.18187/pjsor.v18i4.3955

References

  1. Abid, M., Abbas, N., Nazir, H. Z. and Lin, Z. (2016). Enhancing the mean ratio estimators for estimating population mean using non-conventional location parameters, Revista Colombiana de Estadistica, 39(1), 63–79.
  2. Ali, N., Ahmad, I., Hanif, M.and Shahzad, U. (2021). Robust-regression type estimators for improving mean estimation of sensitive variables by using auxiliary information, Communications in Statistics-theory and Methods, 50(4), 979–992.
  3. Cameron, A. C. and Trivedi, P. K. (1998). Regression Analysis of Count Data, Cambridge University Press, Cambridge.
  4. Kadilar, C., Candan, M. and Cingi, H. (2007). Ratio estimators using robust regression, Hacettepe Journal of Mathematics and Statistics, 36(2), 181–188.
  5. Kadilar,C. and Cingi, H. (2004). Ratio estimators in simple random sampling, Applied Mathematics and Computation, 151(3), 893–902.
  6. Koc, H. (2021). Ratio-type estimators for improving mean estimation using Poisson regression method, Communications in Statistics -theory and Methods, 50(20), 4685–4691.
  7. Koyuncu, N. (2012). Efficient estimators of population mean using auxiliary attributes, Applied Mathematics and Computation, 218(22), 10900–10905.
  8. Montgomery, D. C., Peck, E. A. and Vining, G. G. (2006). Introduction to Linear Regression Analysis, John Wiley and Sons, Hoboken, 4th edition.
  9. Oral, E. and Kadilar, C. (2011a). Improved ratio estimators via modified maximum likelihood, Pakistan Journal of Statistics, 27(3), 269–282.
  10. Oral, E. and Kadilar, C. (2011b). Robust ratio-type estimators in simple random sampling, Journal of the Korean Surgical Society, 40(4),457–467.
  11. Shahzad, U., Perri, P. F. and Hanif, M. (2019). A new class of ratio type estimators for improving mean estimation of non-sensitive and sensitive variables by using supplementary information, Communications in Statistics - Simulation and Computation, 48(9), 2566–2585.
  12. Shahzad, U., Shahzadi, S., Afshan, N., Al-Noor, N.H., Alilah, D. A., Hanif, M. and Anas, M.M. (2021). Poisson
  13. Regression-Based Mean Estimator, Mathematical Problems in Engineering, https://doi.org/10.1155/2021/9769029.
  14. Sisodia, B. V. S. and Dwivedi, V. K. (1981). A modified ratio estimator using coefficient of variation of auxiliary variable, Journal of the Indian Society of Agricultural Statistics, 33(2), 13–18.
  15. Upadhyaya, L. N. and Singh, H. P. (1999). Use of transformed auxiliary variable in estimating the finite population mean, Biometrical Journal, 41(5), 627–636.
  16. Upadhyaya, L. N. Singh, H. P. and Vos, J. W. E. (1985). On the estimation of population means and ratios using supplementary information, Statistical Neerlandica, 39(3),309–318.
  17. Zaman, T. and Bulut, H. (2019). Modified ratio estimators using robust regression methods, Communications in Statistics- Theory and Methods, 48(8), 2039–2048.
  18. Zaman, T. and Bulut, H. (2020). Modified regression estimators using robust regression methods and covariance matrices in stratified random sampling, Communications in Statistics- theory and Methods, 49(14), 3407–3420.
  19. Zaman, T. (2019). Improvement of modified ratio estimators using robust regression method ratio estimators using robust regression methods, Applied Mathematics and Computation, 348, 627–631.