# Linear combination of estimators in probability proportional to sizes sampling to estimate the population

## DOI:

https://doi.org/10.6092/issn.1973-2201/3548## Abstract

In this paper we have studied the gain of efficiency and the relative bias of linear weighted estimators over conventional estimators under probability proportional to size with replacement (ppswr) sampling for a wide variety of populations. The five number summary statistics for the relative bias and the relative efficiency over conventional estimators is given for different magnitude of correlation coefficients. The computational study shows that there is a considerable gain in the efficiency of linear weighted estimators over conventional estimators. To develop the confidence of survey practitioners on linear weighted estimator, the computational study is extended to see the robustness of the linear weighted estimator by deviating the optimum value of the weight up to 50% on either side.## References

S.K. AGARWAL, R.S. KUSHWAHA, B.B.P.S. GOEL (1978), On unequal probability sampling WOR: Theory and Practice, “National Academy of Sciences”, Sp Vol, pp. 251-266.

S.K. AGARWAL, P. KUMAR (1980), Combination of Ratio and PPS estimators, “Journal of Indian Society of Agricultural Statistics”, 32, pp. 81-86.

S.K. AGARWAL, P. KUMAR (1998), On relative efficiency of estimators of population total in PPS sampling when study variable has weak relationship with size variable. “Computational Statistics and Data Analysis”, 28, pp. 271-281.

S.K. AGARWAL, J.A. AL-SALEH, D.K. AL-MUTAIRI (2003), An estimator of population total in multiple characteristics and its robustness to product moment correlation coefficient, “Journal of Statistical Computation and Simulation.”, 73, pp. 377-386.

G.N. AMAHIA, Y.P. CHAUBEY, T.J. RAO (1989), Efficiency of a new estimator in PPS sampling for multiple characteristics, “Journal of Statistical Planning and Inference”, 21, pp. 75-84.

M.L. BANSAL, R. SINGH (1985), An alternative estimator for multiple characteristics in PPS Sampling, “Journal of Statistical Planning andInference”, 11, pp. 313-320.

M.L. BANSAL (1990), An alternative estimator for multiple characteristics in RHC Scheme, “Communications in Statistics – Theory and Methods”, 29, pp. 1777-1784.

A. CHAUDHURI, J.W.E. VOS (1988), Unified Theory and Strategies of Survey Sampling. Elsevier Science Publishers, North Holland.

J.E. FREUND, B.M. PERLES (1999), Statistics: A first course, 7th Ed. Prentice Hall, USA.

W.W. HINES, D.C. MONTGOMERY (1990), Probability and Statistics in Engineering and Management Sciences, 3rd Ed., Prentice Hall.

P. KUMAR, S.K. AGARWAL (1997), Alternative estimators for the population totals in Multiple characteristics surveys. “Communications in Statistics – Theory and Methods”, 26, pp. 2527-2537.

W. MENDENHALL, W. SINCICH, L. TERRY (2003), A second course in statistics: Regression Analysis, 6th Ed. Prentice Hall, New Jersey.

J.S. MILTON, J.C. ARNOLD (2003), Introduction to probability and Statistics for engineers and computing Sciences, McGraw Hill, New York.

M.N. MURTHY (1967), Sampling Theory and Methods. Statistical Publication Society, Calcutta, India.

J. NETER, W. WASSERMANN, M.H. KUTNER (1985), Applied Linear Statistical Models, 2nd Ed. Richard D. Irwin Inc., Illinois.

L. OTT (1984), An introduction to Statistical Methods and Data Analysis, 2nd Ed. Duxbury, Boston.

S. K. PANDEY, R. KARAN SINGH (1984), On Combination of Ratio and PPS estimators, “Biometrical Journal”, 26-3, pp. 333-336.

J.N.K. RAO (1966a), Alternative estimators in PPS sampling for multiple characteristics, “Sankhya”, A 28, pp. 47-60.

J.N.K. RAO (1966b), On the relative efficiency of some estimators in PPS sampling for multiple characteristics, “Sankhya”, A 28, pp. 61-70.

J.N.K. RAO, D.L. BAYLESS (1969), An empirical study of stabilities of estimators and variance estimators in unequal probability sampling. “Journal of American Statistical Association”, 64, pp. 540-549.

D.B. RUBIN, S. WEISBERG (1975), The variance of a linear combination of independent estimators using estimated weights, “Biometrika”, 62, pp. 708 -709.

M.P. SINGH (1978), Alternative estimators in PPS sampling, “Survey Methodology”, 4, pp. 263-271.

M.P. SINGH (1967), Ratio cum product method of estimation. “Metrika”, 12, pp. 21-28.

## Downloads

## Published

## How to Cite

*Statistica*,

*69*(1), 59–71. https://doi.org/10.6092/issn.1973-2201/3548

## Issue

## Section

## License

Copyright (c) 2009 Statistica

This journal is licensed under a Creative Commons Attribution 3.0 Unported License (full legal code).

Authors accept to transfer their copyrights to the journal.

See also our Open Access Policy.