Jackknife variance estimation from complex survey designs

Yıl 2018, Cilt: 47 Sayı: 4, 909 - 919, 01.08.2018

Raghunath Arnab Antonio Arcos

Öz

Large scale surveys very often involve multi-stage sampling design, where the first-stage units are selected with varying probability sampling
without replacement method and the second and subsequent stages units are selected with varying or equal probability sampling schemes. It is well known (vide Chaudhuri and Arnab (1982)) that for such sampling designs it impossible to find an unbiased estimator of the variance of the estimator of the population total (or mean) as a homogeneous quadratic function of the estimators of the totals (means) of second-stage units without estimating variances of the estimators of the totals (means) of the second and sub-sequent stages of sampling. Wolter (1985) has shown that the Jackknife estimators of the population total based on unequal probability sampling overestimates the variance. In this paper we have proposed an alternative Jackknife estimator after reduction of bias from the original Jackknife estimator. The performances of the proposed Jackknife estimator and the original estimator are compared through simulation studies using Household Income and Expenditure Survey (HIES) 2002/03 data collected by CSO, Botswana. The simulation studies reveal that the proposed estimator fares better than the original Jackknife estimator in terms of relative bias and mean-square error.

Anahtar Kelimeler

Complex survey design, Inclusion probability proportional to size, Jackknife estimator, Variance estimation, Varying probability sampling

Kaynakça

• Asok.C. and Sukhatme, B.V. On Sampford's procedure of unequal probability sampling with- out replacement, J. Amer. Statist. Assoc., 71, 912-918, 1976.
• Arnab, R. and North, D. An appraisal of household income and expenditure survey design, Pak. J. Statist., 28, 423-436, 2012.
• Arnab, R., Zewotir, T. and North, D. Variance estimation from complex survey designs: A case study of household income and expenditure survey design 2002/03, Botswana, Com- muni. Statist. Theory. Methods., 44, 63-79, 2015.
• CSO (2005). 2004 Botswana AIDS Impact Survey II
• CSO (2009). 2008 Botswana AIDS Impact Survey III
• CSO (2016). 2012 Botswana AIDS Impact Survey VI (in print)
• Chaudhuri, A. and Arnab, R. On unbiased variance estimation with various multi-stage sampling strategies, Sankhya B, 44, 92-101, 1982.
• CSO Household Income and Expenditure Survey 2002/03, Republic of Botswana, 2004.
• Goodman, R. and Kish, L. Controlled selection-a technique in probability sampling, J. Amer. Statist. Assoc., 45, 350-372, 1950.
• Hartley, H.O and Rao, J.N.K. Sampling with unequal probabilities and without replacement, Ann. Math. Statist., 33, 350-374, 1962.
• Horvitz, D.G. and Thompson, D.J. A generalization of sampling without replacement from a finite universe, J. Amer. Statist. Assoc., 47, 663-685, 1952.
• Sampford, M.R. On sampling without replacement with unequal probability selection, Biometrika, 67, 639-650, 1967.
• Särndal, C.E., Swensson, B. and Wretman, J. Model Assisted Survry Sampling, Springer- Verlag, New York, 1992.
• Singh, H.P., Tailor, R., Singh, S. and Kim, J. M. Estimation of population variance in successive sampling, Quality & Quantity, 45, 477- 494, 2011.
• Singh, S., Horn, S. , and Yu, F. Estimation of variance of the general regression estimator: Higher level calibration approach, Survey Methodology, 24, 41-50, 1998.
• Singh, S., Horn, S., Choudhuri, S. and Yu, F. Calibration of the estimators of variance, Austral. and New Zealand J. Statist. 41, 199-212, 1999.
• Wolter, K. Introduction to variance estimation, Springer-Verlag, New York, 1985.