Abstract
In this paper, a new power transformation estimator of population mean in the presence of non-response has been suggested. The estimator of mean obtained from proposed technique remains better than the estimators obtained from ratio or mean methods of imputation. The mean squared error of the resultant estimator is less than that of the estimator obtained on the basis of ratio method of imputation for the optinum choice of parameters. An estimator for estimating a parameter involved in the process of new method of imputation has been discussed. The MSE expressions for the proposed estimators have been derived analytically and compared empirically. Product method of imputation for negatively correlated variables has also been introduced. The work has been extended to the case of multi-auxiliary information to be used for imputation.
Similar content being viewed by others
References
Bratley P, Fox BL, Schrage LE (1983)A guide to simulation. Springer-Verlag, New York.
Cebrian AA, Garcia MR (1997) Variance estimation using auxiliary information: An almost unbiased multivariate ratio estimator.Metrika, 45, 171–178.
Cochran WG (1977)Sampling Techniques. John Wiley & Sons, New York.
Garcia MR, Cebrian AA (1996) Repeated substitution method: The ratio estimator for the population variance.Metrika, 43, 101–105.
Gunst RF, Mason RL (1980)Regression Analysis and Its Application. A data-oriented approach. New York, Marcel Dekker, Inc.
Heitjan DF, Basu S (1996) Distinguishing ‘Missing at Random’ and ‘Missing Completely at Random’.The American Statistician 50, 207–213.
Horvitz DG, Thompson DJ (1952) A generalisation of sampling without replacement from a finite universe.J. Amer. Statist. Assoc. 47, 663–685.
Lee H, Rancourt E, Sarndal CE (1994). Experiments with variance estimation from survey data with imputed values.J. Official Statist. 10 (3), 231–243.
Meeden G (2000) A decision theoretic approach to imputation in finite population sampling.J. Amer. Statist. Assoc. 95, 586–595.
Murthy MN (1964) Product method of estimation.Sankhya 26, 69–74.
Olkin I (1958) Multi-variate ratio estimation for finite population.Biometrika, 43, 154–163.
Rao JNK, Sitter RR (1995) Variance estimation under two phase sampling with application to imputation for missing data.Biometrika, 82, 453–460.
Reddy VN (1978) A study on the use of prior knowledge on certain population parameters in estimation.Sankhyā C, 40, 29–37.
Rubin DB (1976) Inference and missing data.Biometrika 63(3), 581–592.
Rubin DB (1978).Multiple imputation for non-response in surveys. John Wiley, New York.
Sampath S (1989) On the optimal choice of unknowns in ratio type estimators.J. Indian Soc. Agril. Statist, 41, 166–172.
Singh S (2000a) Estimation of variance of regression estimator in two phase sampling.Calcutta Statist. Assoc. Bull., 50, 49–63.
Singh, S (2000b) Estimation of parametric functions in two-dimensional space in survey sampling.South African J. Statist, 34, 51–71.
Singh S (2001) Generalized calibration approach for estimating the variance in survey sampling.Ann. Ins. Statis. Math. 53(2), 404–417.
Singh S, Horn S (2000) Compromised imputation in survey sampling.Metrika, 51, 267–276.
Singh S, Horn S, Yu, F. (1998). Estimation of variance of general regression estimator: Higher level calibration approach.Survey Methodology, 24(1), 41–50.
Singh S, Horn S, Tracy D (2001). Hybrid of calibration and imputation: Estimation of mean in survey sampling.Statistica, LXI(1), 27–41.
Srivastava SK (1967) An estimator using auxiliary information in sample surveys.Calcutta Statist. Assoc. Bull., 16, 121–132.
Wang SG, Chow SC (1994)Advanced Linear Models: Theory and Applications. New York, Marcel Dekker, Inc.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Singh, S., Deo, B. Imputation by power transformation. Statistical Papers 44, 555–579 (2003). https://doi.org/10.1007/BF02926010
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF02926010