A Family of Estimators of Finite-Population Distribution Function Using Auxiliary Information

详细信息    查看全文

• 作者：Housila P. Singh (1)
  Sarjinder Singh (2)
  Marcin Kozak (3)
  
• 关键词：Auxiliary variate ; Distribution function ; Finite population ; Study variate ; Two ; phase sampling ; 62D05 ; 62P12
• 刊名：Acta Applicandae Mathematicae
• 出版年：2008
• 出版时间：November 2008
• 年：2008
• 卷：104
• 期：2
• 页码：115-130
• 全文大小：338KB
• 参考文献：1. Ahmed, M.S., Abu-Dayyeh, W.: Estimation of finite-population distribution function using multivariate auxiliary information. Stat. Transit. 5(3), 501鈥?07 (2001)
  2. Allen, J., Singh, H.P., Singh, S., Smarandache, F.: A general class of estimators of population median using two auxiliary variables in double sampling. INTERSTAT (2002)
  3. Chaubey, Y.P., Singh, M., Dwivedi, T.D.: A note on an optimality property of the regression estimator. Biom. J. 26(4), 465鈥?67 (1984) CrossRef
  4. Chambers, R.L., Dunstan, R.: Estimating distribution function from survey data. Biometrika 73, 597鈥?04 (1986) CrossRef
  5. Chambers, R.L., Dorfman, A.M., Hall, P.: Properties of the estimators of the finite populations using non-parametric calibration. J. Am. Stat. Assoc. 88, 268鈥?77 (1992) CrossRef
  6. Chambers, R.L., Dorfman, A.M., Wehrly, T.E.: Bias estimation in finite populations using non-parametric calibration. J. Am. Stat. Assoc. 88, 268鈥?77 (1993) CrossRef
  7. Chen, J., Wu, C.: Estimation of distribution function and quantiles using the model-calibrated pseudo empirical likelihood method. Stat. Sin. 12, 1223鈥?239 (2002)
  8. Diana, G.: A class of estimators of the population mean in stratified random sampling. Statistica 53(1), 59鈥?6 (1993)
  9. Dorfman, A.H.: A comparison of design-based and model based estimators of the finite-population distribution function. Aust. J. Stat. 35, 29鈥?1 (1993) CrossRef
  10. Dorfman, A.H.: A note on variance estimation for the regression estimator in double sampling. J. Am. Stat. Assoc. 89, 137鈥?40 (1994) CrossRef
  11. Francisco, C.A., Fuller, W.A.: Quantile estimation with a complex survey design. Ann. Stat. 19, 454鈥?69 (1991) CrossRef
  12. Gupta, P.C.: On some quadratic and higher degree ratio and product estimators. J. Indian Soc. Agril. Stat. 30, 71鈥?0 (1978)
  13. Hidiroglou, M.A., S盲rndal, C.E.: Use of auxiliary information for two-phase sampling. Surv. Method. 24(1), 11鈥?0 (1998)
  14. Johnson, A.A., Breidt, F.J., Opsomer, J.D.: Estimating distribution functions from survey data using nonparametric regression. Preprint Series \#04-07, Department of Statistics, Iowa State University (2004)
  15. Kaur, P.: Generalized unbiased product estimators. Pure Appl. Math. Sci. 17(1鈥?), 67鈥?9 (1983)
  16. Kuk, A.Y.C.: Estimation of distribution functions and median under sampling with unequal probabilities. Biometrika 75, 97鈥?03 (1988) CrossRef
  17. Kuk, A.Y.C.: A kernel method for estimating finite-population distribution functions using auxiliary information. Biometrika 80, 385鈥?92 (1993) CrossRef
  18. Kuk, A.Y.C., Mak, T.K.: Median estimation in the presence of auxiliary information. J. R. Stat. Soc. B 51, 261鈥?69 (1989)
  19. Kulkarni, S.P.: A note on modified ratio estimator using transformation. J. Indian Soc. Agril. Stat. 30(2), 125鈥?28 (1978)
  20. Mak, T.K., Kuk, A.Y.C.: A new method for estimating finite population quantiles using auxiliary information. Can. J. Stat. A 21, 29鈥?8 (1993) CrossRef
  21. Murthy, M.N.: Product method of estimation. Sankhya A 26, 69鈥?4 (1964)
  22. Meeden, G.: Median estimation using auxiliary information. Surv. Method. 21(1), 71鈥?7 (1995)
  23. Meeden, G., Vardeman, S.: A non-informative Bayesian approach to interval estimation in finite population sampling. J. Am. Stat. Assoc. 86, 972鈥?80 (1991) CrossRef
  24. Naik, V.D., Gupta, P.C.: A General class of estimators for estimating population mean using auxiliary information. Metrika 38, 11鈥?7 (1991) CrossRef
  25. Neyman, J.: Contribution to the theory of sampling human population. J. Am. Stat. Assoc. 33, 101鈥?16 (1938) CrossRef
  26. Pandey, G.S.: Product-cum-power estimators. Calcutta Stat. Assoc. Bull. 29, 103鈥?08 (1980)
  27. Randles, R.H.: On the asymptotic normality of statistics with estimated parameters. Ann. Stat. 10, 462鈥?74 (1982) CrossRef
  28. Rao, J.N.K.: Estimating totals and distribution functions using auxiliary information at the estimation stage. J. Off. Stat. 10, 153鈥?65 (1994)
  29. Rao, J.N.K., Kovar, J.G., Mantel, H.J.: On estimating distribution functions and quantiles from survey data using auxiliary information. Biometrika 77(2), 365鈥?75 (1990) CrossRef
  30. Ray, S.K., Sahai, A.: Efficient families of ratio and product type estimators. Biometrika 67, 215鈥?17 (1980) CrossRef
  31. Ray, S.K., Sahai, A., Sahai, A.: A note on ratio and product type estimators. Ann. Inst. Stat. Math. 31, 141鈥?44 (1979) CrossRef
  32. Reddy, V.N.: On a transformed ratio method of estimation. Sankhya C 36, 59鈥?0 (1974)
  33. Robson, D.S.: Application of multivariate polykays to the theory of unbiased ratio-type estimation. J.聽Am. Stat. Assoc. 52, 511鈥?22 (1957) CrossRef
  34. Rueda, M., Arcos, A., Artes, E.: Quantile interval estimation in finite population using multivariate ratio estimator. Metrika 47, 203鈥?13 (1998) CrossRef
  35. Rueda, M., Arcos, A.: On estimating the median from survey data using multiple auxiliary information. Metrika 54, 59鈥?6 (2001) CrossRef
  36. Rueda, M., Arcos, A., Mart铆nez-Miranda, M.D.: Difference estimators of quantile in finite populations. Test 12, 101鈥?16 (2003) CrossRef
  37. Rueda, M., Mart铆nez, S., Mart铆nez, H., Arcos, A.: Estimation of the distribution function with calibration methods. J. Stat. Plan. Inference 137, 435鈥?48 (2007) CrossRef
  38. Sahai, A.: An efficient variant of the product and ratio estimators. Stat. Neerl. 33, 27鈥?5 (1979) CrossRef
  39. Sahai, A., Ray, S.K.: An efficient estimator using auxiliary informations. Metrika 27, 271鈥?75 (1980) CrossRef
  40. Sahoo, J., Sahoo, L.N., Mohanty, S.: A regression approach to estimation in two-phase sampling using two auxiliary variables. Cur. Sci. 65, 73鈥?5 (1993)
  41. Shukla, N.D., Pandey, S.K.: A note on product estimator. Pure Appl. Math. Sci. 15(1鈥?), 97鈥?01 (1982)
  42. Singh, H.P., Espejo, M.R.: On linear regression and ratio-product estimation of a finite population mean. Statistician 52(1), 59鈥?7 (2003)
  43. Singh, S.: Generalized calibration approach for estimating variance in survey sampling. Ann. Inst. Stat. Math. 53(2), 404鈥?17 (2001) CrossRef
  44. Singh, S., Joarder, A.H.: Estimation of the distribution function and median in two-phase sampling. Pak. J. Stat. 18(2), 301鈥?19 (2002)
  45. Singh, S., Joarder, A., Tracy, D.S.: Median estimation using auxiliary information. Aust. N. Z. J. Stat. 43(1), 33鈥?6 (2001) CrossRef
  46. Sisodia, B.V.S., Dwivedi, V.K.: A class of ratio-cum-product type estimators. Biom J. 23(2), 133鈥?39 (1981) CrossRef
  47. Sitter, R.R.: Variance estimation for the regression estimator in two-phase sampling. J. Am. Stat. Assoc. 92(438), 780鈥?87 (1997) CrossRef
  48. Srivastava, S.K.: An estimator using auxiliary information in sample surveys. Calcutta Stat. Assoc. Bull. 6, 121鈥?32 (1967)
  49. Srivenkataramana, T., Tracy, D.S.: An alternative to ratio method in sample surveys. Ann. Inst. Stat. Math. 32, 111鈥?20 (1980) CrossRef
  50. Srivenkataramana, T., Tracy, D.S.: Extending product method of estimation to positive correlation case in surveys. Aust. J. Stat. 23(1), 95鈥?00 (1981) CrossRef
  51. Sukhatme, B.V.: Some ratio-type estimators in two-phase sampling. J. Am. Stat. Assoc. 57, 628鈥?32 (1962) CrossRef
  52. Talukder, M.A.H.: Response bias and difference estimate in double sampling. Metrika 22, 65鈥?5 (1975) CrossRef
  53. Unnikrishnan, N.K., Kunte, S.: Optimality of an analogue of Basu鈥檚 estimator under a double sampling design. Sankhya B 57(1), 103鈥?11 (1995)
  54. Vos, J.W.E.: Mixing of direct, ratio and product method estimators. Stat. Neerl. 34, 209鈥?18 (1980) CrossRef
  55. Walsh, J.E.: Generalization of ratio estimates for population total. Sankhya A 32, 99鈥?06 (1970)
  56. Woodruff, R.S.: Confidence intervals for medians and other position measures. J. Am. Stat. Assoc. 47, 635鈥?46 (1952) CrossRef
  57. Wu, C.: Optimal calibration estimators in surveys sampling. Biometrika 90, 937鈥?51 (2003) CrossRef
  
• 作者单位：Housila P. Singh (1)
  Sarjinder Singh (2)
  Marcin Kozak (3)
  
  1. School of Studies in Statistics, Vikram University, Ujjain, 456010, MP, India
  2. Department of Mathematics, University of Texas at Brownsville and Texas Southmost College, Brownsville, TX, 78520, USA
  3. Department of Experimental Design and Bioinformatics, Faculty of Agriculture and Biology, Warsaw University of Life Sciences, Nowoursynowska 159, 02-776, Warsaw, Poland
  
• ISSN：1572-9036

文摘

This paper considers the problem of estimating the finite-population distribution function and quantiles with the use of auxiliary information at the estimation stage of a survey. We propose the families of estimators of the distribution function of the study variate y using the knowledge of the distribution function of the auxiliary variate x. In addition to ratio, product and difference type estimators, many other estimators are identified as members of the proposed families. For these families the approximate variances are derived, and in addition, the optimum estimator is identified along with its approximate variance. Estimators based on the estimated optimum values of the unknown parameters used to minimize the variance are also given with their properties. Further, the family of estimators of a finite-population distribution function using two-phase sampling is given, and its properties are investigated.