An Empirical Comparison of Some Product Estimators
Keywords:auxiliary variable, prediction approach, product estimator
In this paper, we undertake an extensive comparative study of some biased, almost unbiased and unbiased product estimators on the ground of different performance measures through Monte Carlo simulation that has not yet been initiated in the survey sampling literature. The simulation experiment is conducted using data on 20 natural populations available in the literature, and the performance indicators taken into consideration are the absolute relative bias, percentage relative efficiency, coverage rate of confidence intervals, standard deviation of the student t-statistic, and approach to symmetry (normality). This empirical study will not only facilitate to assess the overall relative performance of different competing product or product-type estimators but will also be beneficial to provide some guidelines towards further research in this direction.
Basu, D. (1971). An essay on the logical foundations of survey sampling. Foundations of Statistical Inference, Vol. I, V. P. Godambe & D. A. Sprott, eds., Holt, Rinehart and Wintson, Toronto, Canada, 203â€“242.
Bhuyan, K.C. (2005). Multivariate Analysis and its Applications. New Central Book Agency (P) Ltd, Kolkata.
Bolfarine, H. and Zacks, S. (1992). Prediction Theory for Finite Populations. Springer-Verlag.
Chaubey, Y. P., Dwivedi, T. D. and Singh, M. (1990). On the exact variance of an unbiased product-type estimator and its comparison with the sample mean. Metrika, 37, 255-262.
Gujarati, D.N. and Porter, D.C. (2009). Basic Econometrics (5th Edition). McGraw-Hill, New York, NY, 10020.
Gupta, P.C. and Adhvaryu, D. (1982). On some unbiased product-type strategies. Journal of the Indian Society of Agricultural Statistics, 34, 48-54.
Johnson, R.A. and Wichern, D.W. (2007). Applied Multivariate Statistical Analysis. Pearson Education, Inc., New Jersey.
Maddala, G.S. (1992). Introduction to Econometrics (2nd Edition). Macmillan Publishing Company, New York.
Montgomery, D.C., Peck, E.A. and Vining, G.G. (2012). Introduction to Linear Regression Analysis (5th Edition). John Wiley & Sons, Inc.
Morrison, D.F. (1990). Multivariate Statistical Methods (3rd Edition). McGraw-Hill Publishing Company, New York.
Murthy, M. N. (1964). Product method of estimation. Sankhya, 26, 69-74.
Quenouille, M.H. (1956). Notes on bias in estimation. Biometrika, 43, 353-360.
Rao, J.N.K. (1969). Ratio and regression estimators. New Developments in Survey Sampling. N.L. Johnson and H. Smith Jr. (eds.), Chapel Hill, North Carolina, 213-234.
Rawlings, J.O., Pantula, S.G. and Dickey, D.A. (1998). Applied Regression Analysis (2nd Edition). Springer-Verlag, New York, Inc.
Rencher, A.C. (2002). Methods of Multivariate Analysis (2nd Edition). John Wiley & Sons, Inc.
Robson, D.S. (1957). Application of multivariate polykays to the theory of unbiased ratio-type estimators. Journal of the American Statistical Association, 52, 511-522.
Sahoo, J. and Sahoo, L.N. (1999). On two almost unbiased product estimators. Journal of the Indian Society of Agricultural Statistics, 1999, 52, 222-227.
Sahoo, J., Sahoo, L.N. and Mohanty, S. (1995). Empirical comparison of some regression and regression-type strategies. Statistical Papers, 36, 337-347.
Sahoo, L.N. (1983). On a method of bias reduction in ratio estimation. Journal of Statistical Research, 16, 1-6.
Sahoo, R.K., Sabat, Ajit Kumar and Sahoo, L.N. (2022). On a method of bias reduction in the product method of estimation. Asian Journal of Probability and Statistics, 16, 26-35.
Sampford (1978). Predictive estimation and internal congruency. Contribution to Survey Sampling and Applied Statistics, H. A. David, ed., Academic Press, New York, 29â€“39.
Shukla, N.D. (1976). Almost unbiased product-type estimator. Metrika, 23, 127-133.
Singh, H. P. (1989). A class of unbiased estimators of product of population means. Journal of Indian Society of Agricultural Statistics, 41, 113-118.
Srivastava, S.K. (1983). Predictive estimation of finite population using product estimators. Metrika, 30, 93-99.
Srivastava, V. K., Shukla, N. D. and Bhatnagar, S. (1981). Unbiased product estimators. Metrika, 52, 191-196.