Effective rotation patterns for median  estimation in successive sampling

Kumari Priyanka; Richa Mittal

doi:https://doi.org/10.59170/stattrans-2014-014

Effective rotation patterns for median estimation in successive sampling

Kumari Priyanka Department of Mathematics, Shivaji College (University of Delhi), New Delhi – 110027, India , Richa Mittal Department of Mathematics, Shivaji College (University of Delhi), New Delhi – 110027, India. Statistics in Transition new series, vol. 15, 2014, 2, pages: 197-220 Published online: 2 June 2014 https://doi.org/10.59170/stattrans-2014-014

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ABSTRACT

The present work deals with the problem of estimation of population median at current occasion in two-occasion successive sampling. Best linear unbiased estimators have been proposed by utilizing additional auxiliary information, readily available on both the occasions. Asymptotic variances of the proposed estimators are derived and the optimum replacement policies are discussed. The behaviours of the proposed estimators are analyzed on the basis of data from natural populations. Simulation studies have been carried out to measure the precision of the proposed estimators

KEYWORDS

population median, successive sampling, auxiliary information, optimum replacement policy

REFERENCES

ARNAB, R., OKAFOR, F. C., (1992). A note on double sampling over two occasions. Pakistan JNL of statistics 8, 9–18.

BANDYOPADHYAY, A., SINGH, G. N., (2014). On the use of two auxiliary variables to improve the precision of estimate in two-occasion successive sampling. International Journal of Mathematics and Statistics15(1): 73–88.

CHAMBERS, R. L., DUNSTAN, R., (1986). Estimating distribution functions from survey data. Biometrika 73, 597–604.

ECKLER, A. R., (1955). Rotation Sampling. Ann. Math. Statist.: 664–685.

FENG, S., ZOU, G., (1997). Sample rotation method with auxiliary variable. Commun. Statist. Theo-Meth.26: 6, 1497–1509.

GORDON, L., (1983). Successive sampling in finite populations. The Annals of statistics 11(2): 702–706.

GROSS, S. T., (1980). Median estimation in sample surveys. Proc. Surv. Res. Meth. Sect. Amer. Statist. Assoc.: 181–184.

GUPTA, S., SHABBIR, J., AHMAD, S., (2008). Estimation of median in two phase sampling using two auxiliary variables. Communications in Statistics -Theory & Methods 37(11): 1815–1822.

JESSEN, R. J., (1942). Statistical investigation of a sample survey for obtaining farm facts. Iowa Agricultural Experiment Station Road Bulletin No. 304, Ames: 1–104.

KHOSHNEVISAN, M., SAXENA, S., SINGH, H. P., SINGH, S., SMARANDACHE, F., (2002). Randomness and optimal estimation in data sampling. American Research Press, Second Edition, Rehoboth.

KUK, A. Y. C., MAK, T. K., (1989). Median estimation in presence of auxiliary information. J. R. Statit. Soc. B, 51: 261–269.

MARTINEZ-MIRANDA, M. D., RUEDA-GARCIA, M., ARCOS-CEBRIAN, A., ROMAN-MONTOYA, Y., GONZAEZ-AGUILERA, S., (2005). Quintile estimation under successive sampling. Computational Statistics, 20:385–399.

NARAIN, R. D., (1953). On the recurrence formula in sampling on successive occasions. Journal of the Indian Society of Agricultural Statistics 5: 96–99.

PATTERSON, H. D., (1950). Sampling on successive occasions with partial replacement of units. Jour. Royal Statist. Assoc., Ser. B, 12: 241–255.

RAO, J. N. K., KOVAR, J. G., MANTEL, H. J., (1990). On estimating distribution functions and quantiles from survey data using auxiliary information. Biometrika, 77: 2, 365–375.

RUEDA, M. D. M., ARCOS, A., ARTES, E., (1998). Quantile interval estimation in finite population using a multivariate ratio estimator. Metrika 47: 203–213.

RUEDA, M. D. M., MUNOZ, J. F., (2008). Successive sampling to estimate quantiles with P-Auxiliary Variables. Quality and Quantity, 42:427–443.

SEDRANSK, J., MEYER, J., (1978). Confidence intervals for quantiles of a finite population: Simple random and stratified simple random sampling. J. R.Statist. Soc., B, 40: 239–252.

SILVERMAN, B. W., (1986). Density Estimation for Statistics and Data Analysis, Chapman and Hall, London.

SINGH, G. N., SINGH, V. K., (2001). On the use of auxiliary information in successive sampling. Jour. Ind. Soc. Agri. Statist. 54(1): 1–12.

SINGH, G. N., PRIYANKA, K., (2008). Search of good rotation patterns to improve the precision of estimates at current occasion. Communications in Statistics (Theory and Methods) 37(3), 337–348.

SINGH, G. N., PRASAD, S., MAJHI, D., (2012). Best Linear Unbiased Estimators of Population Variance in Successive Sampling. Model Assisted Statistics and Applications, 7, 169–178.

SINGH, H. P., TAILOR, R., SINGH, S., JONG-MIN KIM, (2007). Quintile estimation in successive sampling, Journal of the Korean Statistical Society, 36: 4, 543–556.

SINGH, H. P., SOLANKI, R. S., (2013). Some Classes of estimators for population median using auxiliary information. Communications in Statistics - Theory & Methods, 42, (23), 4222–4238.

SINGH, S., (2003). Advanced Sampling Theory with Applications; How Michael ‘selected’ Amy. (Vol. 1 and 2) pp. 1–1247, Kluwer Academic Publishers, The Netherlands.

SMITH, P., SEDRANSK, J., (1983). Lower bounds for confidence coefficients for confidence intervals for finite population quantiles. Communications in Statistics - Theory & Methods, 12: 1329–1344