Generalized class of synthetic estimators for small areas under systematic sampling scheme

Krishan K. Pandey; G. C. Tikkiwal

doi:https://doi.org/10.59170/stattrans-2010-005

Generalized class of synthetic estimators for small areas under systematic sampling scheme

Krishan K. Pandey Assistant Professor, CMES, University of Petroleum & Energy Studies, Dehradun- 248007, India. , G. C. Tikkiwal Department of Mathematics & Statistics, J.N.V. University, Jodhpur, Rajasthan -342011, India Statistics in Transition new series, vol. 11, 2010, 1, pages: 75-89 Published online: 1 July 2010 https://doi.org/10.59170/stattrans-2010-005

75 Views 3 Downloads

ARTICLE

(English) PDF

ABSTRACT

This paper defines and discusses a generalized class of synthetic estimators for small domain, using auxiliary information, under systematic sampling scheme. The generalized class of synthetic estimators, among others, includes the simple, ratio and product synthetic estimators. Further, it demonstrates the use of the generalized synthetic and ratio synthetic estimators for estimating crop acreage for small domain and also compares their relative performance with direct estimators, empirically, through a simulation study.

KEYWORDS

Synthetic Estimation; Small Domain; Inspector Land Revenue Circles (ILRCs); Timely Reporting Scheme (TRS); Absolute Relative Bias (ARB); Simulated relative standard error (Srse).

REFERENCES

GHANGURDE, P.D. and SINGH, M.P. (1978).“Evaluation of efficiency of synthetic estimates”, Proceeding of the Social Statistical Section of the American Statistical Association, 53–61.

COCHRAN, W.G. (1977).“Sampling Techniques”, Wiley & Sons.

GONZALEZ, M.E. (1973). “Use and evaluation of synthetic estimates”, Proceedings of the social statistical section of American Statistical Association, 33–36.

GONZALEZ, M. E. and WAKSBERG, J. (1973).“Estimation of the error of synthetic estimates”, paper presented at first meeting of the International association of survey statisticians, Vienna, Austria, 18–25, august 1973.

LAHIRI, D.B. (1954).“On the question of bias of systematic sampling”, Proceedings of the world Population Conference, 6, 349–62.

MURPHY, K.E. CARTER, C.M. & WOLFE, L.H. (2001) “How long should I simulate, and for how many trials? A practical guide to reliability simulations”, Reliability and Maintainability Symposium, 2001, Proceedings, Philadelphia, p.p. 207–212.

MADOW, L.H. (1946).“Systematic sampling and its relation to other sampling designs”, Journal of American Statistical Association 41:204–217.

Osborne, J.G. (1942).“Sampling errors of systematic & random survey of covertype areas”, Journal of American Statistical Association 37:256–264.

SRIVASTAVA, S.K. (1967). “An estimator using auxiliary information in sample surveys”, Calcutta Statist. Assoc. Bull. , 121–132.

SWAIN, A.K.P.C. (1964).“The use of systematic sampling in ratio estimates”, JISA, 2, 160–164.

SUKHATME, P. V. SUKHATME, B. V., SUKHATME, S. and ASOK, C. (1984). “Sampling Theory of Surveys with Applications (3rd Edition)”, Indian Society of Agricultural Statistics, New Delhi.

TIKKIWAL, G.C. and GHIYA, A. (2000). “A generalized class of synthetic estimators with application of crop acreage estimation for small domains”, Biom, J, 42, 7, 865–876.

TIKKIWAL, B.D. (1993). “Modelling through survey data for small domains”, Proceedings of International Scientific conference on small area statistics and survey Design (held in September, 1992 at Warsaw, Poland).

TIKKIWAL, G.C. and PANDEY, K.K. (2007).“On Synthetic and Composite Estimators for Small Area Estimation under Lahiri – Midzuno Sampling Scheme”, Statistics in Transition New Series, vol. 8. No. 1, 111–123.

WOLTER, K.M. (1984, 1985).“An investigation of some estimators of variances for systematic sampling”, J. Amer. Stat. Assoc., 79, 781–90.

WHITT, W. (1989).“Simulation run length planning”, in the proceedings of the 1989 winter simulation conference, AT & T Bell laboratories U.S.A., pp- 106–112.