Communications for Statistical Applications and Methods

The Korean Statistical Society (한국통계학회)
권호 표지
DOI QR코드

DOI QR Code

A General Procedure for Estimating the General Parameter Using Auxiliary Information in Presence of Measurement Errors

  • Singh, Housila P. (School of Studies in Statistics, Vikram University) ;
  • Karpe, Namrata (School of Studies in Statistics, Vikram University)
  • Published : 2009.09.30
Download PDF
⟨ Previous Next ⟩

Abstract

This article addresses the problem of estimating a family of general population parameter ${\theta}_{({\alpha},{\beta})}$ using auxiliary information in the presence of measurement errors. The general results are then applied to estimate the coefficient of variation $C_Y$ of the study variable Y using the knowledge of the error variance ${\sigma}^2{_U}$ associated with the study variable Y, Based on large sample approximation, the optimal conditions are obtained and the situations are identified under which the proposed class of estimators would be better than conventional estimator. Application of the main result to bivariate normal population is illustrated.

Keywords

References

  1. Allen, J., Singh, H. P. and Smarandache, F. (2003). A family of estimators of population mean using multiauxiliary information in presence of measurement errors, International Journal of Social Economics, 30, 837-849 https://doi.org/10.1108/03068290310478775
  2. Birch, M. W. (1964). A note on the maximum likelihood estimation of a linear structural relationship, Journal of the American Statistical Association, 59, 1175-1178 https://doi.org/10.2307/2282631
  3. Cheng, C. L. and Van Ness, J. W. (1991). On the unreplicated ultra structural model, Biometrika, 78, 442-445 https://doi.org/10.1093/biomet/78.2.442
  4. Cheng, C. L. and Van Ness, J. W. (1994). On estimating linear relationships when both variables are subject to errors, Journal of the Royal Statistical Society, Series B., 56, 167-183
  5. Cochran, W. G (1968). Errors of measurement in statistics, Technometrics, 10, 637-666 https://doi.org/10.2307/1267450
  6. Das, A. K. and Tripathi, T. P. (1977). Admissible estimators for quadratic forms in finite populations, Bulletin of the International Statistical Institute, 47, 132-135
  7. Das, A. K. and Tripathi, T. P. (1978). Use of auxiliary information in estimating the finite population variance, Sankhya Series C, 40, 139-148
  8. Das, A. K. and Tripathi, T. P. (1981). A class of sampling strategies for population mean using information on mean and variance of an auxiliary character, In Proceedings of the Indian Sta-tistical Institute Golden Jubilee International conference on Statistics: Applications and New Directions, Calcutta 16 December-19 December, 1981, 174-181
  9. Das, A. K. and Tripathi, T. P. (1992-1993). Use of auxiliary information in estimating the coefficient of variation, Ali Garh Journal of Statistics, 12 & 13, 51-58
  10. Fuller, W. A. (1987). Measurement Errors Models, John Wiley & Sons, New York
  11. Liu, T. P. (1974). A general unbiased estimator for the variance of a finite population, Sankhya Series C, 36, 23-32
  12. Manisha and Singh, R. K. (2001). An estimation of population mean in the presence of measurement error, Journal of Indian Society of Agricultural Statistics, 54, 13-18
  13. Maneesha and Singh, R. K. (2002). Role of regression estimator involving measurement errors, Brazilian Journal of Probability and Statistics, 16, 39-46
  14. Schneewei\beta, H. M. (1976). Consistent estimation of a regression with errors in the variables, Metrika, 23, 101-105 https://doi.org/10.1007/BF01902854
  15. Searls, D. T. (1964). The utilization of a known coefficient of variation in the estimation procedure, Journal of American Statistical Association, 59, 1225-1226
  16. Searls, D. T. and Interapanich, P. (1990). A note on an estimator for the variance that utilizes the kurtosis, The American Statistician, 44, 195-296 https://doi.org/10.1080/00031305.1990.10475717
  17. Shalabh (1997). Ratio method of estimation in the presence of measurement errors, Journal of Indian Society of Agricultural Statistics, 52, 150-155
  18. Shalabh (2000). Predictions of values of variables in linear measurement error model, Journal of Applied Statistics, 27, 475-482 https://doi.org/10.1080/02664760050003650
  19. Singh, H. P. (1986). A generalized class of estimators of ratio, product and mean using supplementary information on an auxiliary character in PPSWR sampling scheme, Gujarat Statistical Review, 13, 1-30
  20. Singh, H. P. and Karpe, N. (2008a). Ratio-Product estimator for population mean in presence of measurement errors, Journal of Applied Statistical Science, 16, 49-64
  21. Singh, H. P. and Karpe, N. (2008b). Estimation of population variance using auxiliary information in the presence of measurement errors, Statistics in Transition, 9, 443-470
  22. Singh, H. P. and Karpe, N. (2009). A class of estimators using auxiliary information for estimating finite population variance in presence of Measurement Errors, Communications in Statistics - Theory and Methods, 38, 734-741 https://doi.org/10.1080/03610920802290713
  23. Singh, H. P., Upadhyaya, L. N. and Nomjoshi, U. D. (1988). Estimation of finite population variance, Current Science, 57, 1331-1334
  24. Singh, H. P., Upadhyaya, L. N. and Iachan, R. (1990). An efficient class of estimators using supple-mentary information in sample surveys, Ali Garh Journal of Statistics, 10, 37-50
  25. Singh, J., Pandey, B. N. and Hirano, K. (1973). On the utilization of a known coefficient of kurtosis in the estimating procedure of variance, Annals of the Institute of Statistical Mathematics, 25, 51-55 https://doi.org/10.1007/BF02479358
  26. Srivastava, A. K. and Shalabh (1997). Asymptotic efficiency properties of least square in an ultra-structural model, Test, 6, 419-431 https://doi.org/10.1007/BF02564707
  27. Srivastava, A. K. and Shalabh (2001). Effect of measurement errors on the regression method of estimation in survey sampling, Journal of Statistical Research, 35, 35-44
  28. Srivastava, S. K. (1971). A generalized estimator for the mean of a finite population using multi-auxiliary information, Journal of the American Statistical Association, 6, 404-407
  29. Srivastava, S. K. (1980). A class of estimators using auxiliary information in sample surveys, Cana-dian Journal of Statistics, 8, 253-254 https://doi.org/10.2307/3315237
  30. Srivastava, S. K. and Jhajj, H. S. (1980). A class of estimators using auxiliary information for esti-mating finite population variance, Sankhya Series C, 4, 87-96
  31. Srivastava, S. K. and Jhajj, H. S. (1981). A class of estimating of the population mean in survey sampling using auxiliary information, Biometrika, 68, 341-343 https://doi.org/10.1093/biomet/68.1.341
  32. Sud, C. and Srivastava, S. K. (2000). Estimation of population mean in repeat surveys in the presence of measurement errors, Journal of Indian Society of Agricultural Statistics, 53, 125-133
  33. Tripathi, T. P, Singh, H. P. and Upadhyaya, L. N. (2002). A general method of estimation and its application to the estimation of coefficient of variation, Statistics in Transition, 5, 887-908
  34. Upadhyaya, L. N. and Singh, H. P. (1999). Use of transformed auxiliary variable in estimating the finite population mean, Biometrical Journal, 41, 627-636 https://doi.org/10.1002/(SICI)1521-4036(199909)41:5<627::AID-BIMJ627>3.0.CO;2-W
  35. Upadhyaya, L. N. and Singh, H. P. (2001). Estimation of the population standard deviation using auxiliary information, American Journal of Mathematical and Management Sciences, 21, 345-358

Cited by

  1. Finite Population Variance Estimation in Presence of Measurement Errors vol.41, pp.23, 2012, https://doi.org/10.1080/03610926.2011.573165