Abstract
Design-based and design-based model-assisted estimator of total for a variable having many zero values has high variance. The censored regression (tobit) model-based estimators of a finite-population total have been proposed earlier. The aim of the current research is to apply the semiparametric model to a variable with many zero values, to estimate the population total by model-based and model-assisted estimators, and to compare them with other known estimators by simulation.
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References
T. Amemiya, Tobit models: A survey, J. Econom., 24:3–61, 1984.
A. Arabmazar and P. Schmidt, An investigation of the robustness of the tobit estimator to non-normality, Econometrica, 50:1055–1063, 1982.
V. Bentkus, G.D.C. Gueze, and M.C.A. van Zuijlen, Optimal Hoeffding-like inequalities under a symmetry assumption, J. Theor. Appl. Stat., 40(2):159–164, 2006.
D.A. Binder and G.R. Roberts, Design-based and model-based methods for estimating model parameters, in R.L. Chambers and C.J. Skinner (Eds.), Analysis of Survey Data, John Wiley & Sons Ltd, Chichester, 2003, pp. 29–48.
F.J. Breidt, G. Claeskens, and J.D. Opsomer, Model-assisted estimation for complex surveys using penalized splines, Biometrika, 92(4):831–846, 2005.
F.J. Breidt and J.D. Opsomer, Local polynomial regression estimators in survey sampling, Ann. Stat., 28(4):1026–1053, 2000.
F.J. Breidt and J.D. Opsomer, Nonparametric and semiparametric estimation in complex surveys, in C.R. Rao and D. Pfeffermann (Eds.), Handbook of Statistics – Sample Surveys: Inference and Analysis, Vol. 29B, Elsevier, North-Holland, Amsterdam, 2009, pp. 103–119.
F.J. Breidt, J.D. Opsomer, A.A. Johnson, and M.G. Ranalli, Semiparametric model-assisted estimation for natural resource surveys, Surv. Methodol., 33(1):35–44, 2007.
R.L. Chambers, A.H. Dorfman, and M.Yu. Sverchkov, Nonparametric regression with complex survey data, in R.L. Chambers and C.J. Skinner (Eds.), Analysis of Survey Data, JohnWiley & Sons Ltd, Chichester, 2003, pp. 151–174.
K.Y. Chay and J.L. Powell, Semiparametric censored regression models, J. Econ. Perspect., 15(4):29–42, 2001.
J. Chen, S.-Y. Chen, and J.N.K. Rao, Empirical likelihood confidence intervals for the mean of a population containing many zero values, Can. J. Stat., 31(1):53–68, 2003.
W. Cochran, Sampling Techniques, John Wiley & Sons, New York, 1977.
A. Deaton and M. Irish, Statistical models for zero expenditures in household budgets, J. Publ. Econ., 23:59–80, 1984.
A.H. Dorfman, Non-parametric regression for estimating totals in finite populations, in Proceedings of the Section on Survey Research Methods, American Statistical Association, 1992, pp. 622–625.
B. Ganguli and M.P.Wand, SemiPar 1.0 Users’ Manual, 2009, available from: http://cran.r-project.org [cited 7 February 2011].
C. Goga, Reduction de la variance dans les sondages en presence d’information auxiliaire: une approche non parametrique par splines de regression (Variance reduction in surveys with auxiliary information: A nonparametric approach involving regression splines), Can. J. Stat., 33(2):163–180, 2005.
W.H. Greene, Econometric Analysis, Prentice Hall, Upper Saddle River, 2003.
F. Karlberg, Survey Estimation for Highly Skewed Data, PhD Dissertation, Stockholm University, Stockholm, 1999.
F. Karlberg, Survey estimation for highly skewed populations in the presence of zeroes, J. Offic. Stat., 3(2):229–241, 2000.
D. Krapavickaitė, Estimation of a finite population total for a censored regression model for a study variable, Acta Appl. Math., 96(1–3):339–347, 2007, available from: http://dx.doi.org/10.1007/s10440-007-9099-9 [cited February 7, 2011].
D. Krapavickaitė, Model-based estimator of total expenditure on environmental protection, Math. Model. Anal., 12(3):369–377, 2007.
R. Lehtonen and A. Veijanen, Logistic generalized regression estimators, Surv. Methodol., 24(1):51–55, 1998.
G.E. Montanari and M.G. Ranalli, Nonparametric model calibration estimation in survey sampling, J. Am. Stat. Assoc., 100(472):1429–1442, 2005.
J.A. Nelder and R. Mead, A simplex method for function minimization, Comput. J., 7:308–313, 1965.
J.D. Opsomer, F.J. Breidt, G.G. Moisen, and G. Kauermann, Model assisted estimation of forest resources with generalized additive models, J. Am. Stat. Assoc., 102(478):400–416, 2007.
J.L. Powell, Least absolute deviations estimation for the censored regression model, J. Econom., 25:303–325, 1984.
R Development Core Team, R: A Language and Environment for Statistical Computing, Reference Index, Version 2.12.1 (2010-10-16), R Foundation for Statistical Computing, Vienna, Austria, 2008, available from: http://www.R-project.org [cited 7 February 2011].
D. Ruppert, M.P. Wand, and R.J. Carroll, Semiparametric Regression, Cambridge Univ. Press, Cambridge, 2003.
C.E. Sarndal, B. Swensson, and J. Wretman, Model Assisted Survey Sampling, Springer, New York, 1992.
J. Tobin, Estimation of relationships for limited dependent variables, Econometrica, 26:24–36, 1958.
R. Valliant, Nonlinear prediction theory and the estimation of proportions in a finite population, J. Am. Stat. Assoc., 80(391):631–641, 1985.
R. Valliant, A.H. Dorfman, and R.M. Royall, Finite Population Sampling and Inference: A Prediction Approach, John Wiley & Sons, New York, 2000.
C. Wu and R.R. Sitter, A model calibration approach to using complete auxiliary information from survey data, J. Am. Stat. Assoc., 96(453):185–193, 2001.
H. Zheng and R.J.A. Little, Penalized spline model-based estimation of finite population total from probabilityproportional-to-size samples, J. Offic. Stat., 19(2):99–107, 2003.
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Krapavickaitė, D. Some models for estimation of total of a study variable having many zero values. Lith Math J 51, 370–384 (2011). https://doi.org/10.1007/s10986-011-9133-5
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DOI: https://doi.org/10.1007/s10986-011-9133-5