On non-negative and improved variance estimation for the ratio estimator under the Midzuno-Sen sampling scheme

Jigna Patel; P. A. Patel

doi:https://doi.org/10.59170/stattrans-2009-028

On non-negative and improved variance estimation for the ratio estimator under the Midzuno-Sen sampling scheme

Jigna Patel Department of Statistics, Sardar Patel University, Vallabh Vidhyanagar-388120, Gujarat, India , P. A. Patel Department of Statistics, Sardar Patel University, Vallabh Vidhyanagar-388120, Gujarat, India Statistics in Transition new series, vol. 10, 2009, 3, pages: 371-385 Published online: 1 December 2009 https://doi.org/10.59170/stattrans-2009-028

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ABSTRACT

Various studies on variance estimation showed that it is hard to single out a best and non-negative variance estimator in finite population. This paper attempts to find improved variance estimators for the ordinary ratio estimator under the Midzuno-Sen sampling scheme. A Monte Carlo comparison has been carried out. The suggested estimator has performed well and has taken non-negative values with probability 1.

KEYWORDS

Model-based estimation, Monte Carlo Simulation, Ratio estimator, Variance estimation

REFERENCES

BREWER, K.R.W. and TAM, S.M. (1990). Is the assumption of uniform intraclass correlation ever justified? Australian Journal of Statistics, 32(3), 411– 423.

CASSEL, C. M., SÄRNDAL, C. E. and WRETMAN, J. H. (1977). Foundation of Inference in Survey Sampling, John Wiley, New York.

CHAUDHURI, A. (1975). On some inference problems with finite populations and related topics in survey sampling theory. Economic Statistics Papers. No.10, 1975, University of Sydney.

CHAUDHURI, A. (1976). A non-negativity criterion for a certain variance estimator. Metrika, 23, 201–205.

CHAUDHURI, A. (1981). Non- negative unbiased variance estimators. Current topics in survey sampling, Academic Press, Inc., 317–328.

CHAUDHURI, A. and ARNAB, R. (1981). On non- negative variance estimation. Metrika, 28, 1–12.

DENG, L.Y. and WU, C.F.J. (1987). Estimation of the regression estimator. Journal of American Statistical Association, 82, 568–576.

GUJARATI, D. N. (1995). Basic Econometrics, McGraw-Hill, Inc.

ISAKI, C. T. and FULLER (1982). Survey Design under the regression superpopulation model, Journal of the American Statistical Association, 7, 89–96 KREWSKI, D. and CHAKRABARTY, R. P. (1981). On the stability of the

jackknife variance estimator in ratio estimation. Journal of Statistical Planning and Inference, 5, 71–78.

MIDZUNO, H. (1950). An outline of the theory of sampling systems. Annals Institute of Statistics and Mathematics, Tokyo, 1, 149–156.

MONTGOMERY, D. C.; PECK, E. A. and VINING, G. G. (2003). Introduction to linear regression analysis. Third Edition, John Wiley & Sons, Inc.

MUKHOPADHYAY, P. (1996). Inferential Problems in Survey Sampling, New Age International, New Delhi.

MURTHY, M. N. (1967). Sampling Theory and Methods. Calcutta: Statistical Publishing Society.

PATEL, P. A. and SHAH, D. N. (1999). Model-based estimation for a finite population variance. Journal of the Indian Statistical Association, 37(1), 27– 35.

RAO, J. N. K. (1968). Some small sample results in ratio and regression Estimation. Journal of the Indian Statistical Association, 6, 160–168.

RAO, J. N. K. (1969). Ratio and regression estimators, in new developments in Survey Sampling (N.L.John and H. Smith, eds.), Wiley, New York, 213–234.

RAO, J. N. K. (1979). On deriving mean square errors and their non-negative unbiased estimators in finite population sampling. Journal of the Indian Statistical Association, 17, 125–136.

RAO, J. N. K. and BEEGLE, L. D. (1967). A Monte Carlo study of some ratio Estimators. Sankhya, Series B, 29, 47–56.

RAO, J. N. K. and KUZIK, R. A. (1974). Sampling errors in ratio estimation. Sankhya, Series C, 36 (1974), 43–58.

RAO, J.N.K. and VIJAYAN, K. (1977). On estimating the variance in sampling with probability proportional to aggregate size. Journal of the American Statistical Association, 72, 579–584.

RAO, P.S.R.S. and RAO, J.N.K. (1971). Small sample results for ratio estimators. Biometrika, 58, 625–630.

RAO, T. J. (1972). On the variance of the ratio estimator for the Midzuno-Sen Sampling scheme. Metrika, 18, 209–215.

RAO, T. J. (1977). Estimating the variance of the ratio estimator for the Midzuno- Sen sampling scheme. Metrika, 24, 203–215.

ROYALL, R.M. and CUMBERLAND, W.G. (1978). Variance estimation in finite population sampling. Journal of the American Statistical Association, 73, 351–358.

ROYALL, R.M. and CUMBERLAND, W.G. (1981). An empirical study of the ratio estimator and estimators of its variance. Journal of the American Statistical Association, 76, 355–359.

ROYALL, R.M. and EBERHADT, K.R. (1975). Variance estimates for ratio estimator. Sankhya, Series C, 37, 43–52.

TRACY, D. S. and MUKHOPADHYAY, P. (1994). On non-negative unbiased variance estimation for Midzuno strategy, Pak. J. Stat., 10 (3), 575–583.

VALLIANT R, DORFAM, A.H., ROYALL, R.M. (2000). Finite population sampling and inference, Wiley, New York.

VIJAYAN, K., MUKHOPADHYAY, P. and BHATTACHARYA, S. (1995). On non-negative unbiased estimation of quadratic forms in finite population, Australian Journal of Statistics, 37 (2), 168–178.

WU, C. F. J. (1982). Estimation of variance of the ratio estimator. Biometrika, 69, 183–189.

WU, C.F.J. and DENG, L.(1983). Estimation of variance of the ratio estimator: An empirical study. In Scientific Inference Data Analysis and Robustness.