A New Method to Estimate the Low Income Proportion: Monte Carlo Simulations

Estimation of a proportion has many applications in
economics and social studies. A common application is the estimation
of the low income proportion, which gives the proportion of people
classified as poor into a population. In this paper, we present this
poverty indicator and propose to use the logistic regression estimator
for the problem of estimating the low income proportion. Various
sampling designs are presented. Assuming a real data set obtained
from the European Survey on Income and Living Conditions, Monte
Carlo simulation studies are carried out to analyze the empirical
performance of the logistic regression estimator under the various
sampling designs considered in this paper. Results derived from
Monte Carlo simulation studies indicate that the logistic regression
estimator can be more accurate than the customary estimator under
the various sampling designs considered in this paper. The stratified
sampling design can also provide more accurate results.

• Encarnación Álvarez
• Rosa M. García-Fernández
• Juan F. Muñoz

[1] E. A´ lvarez, R.M. Garc´ıa-Ferna´ndez, J.F. Mun˜oz and F.J. Blanco-
Encomienda, "On estimating the headcount index by using the logistic
regression estimator”. International Journal of Mathematical, Computational,
Physical and Quantum Engineering, 8(8),pp. 1039–1041, 2014.
[2] J. Chen and R.R. Sitter, ”A pseudo empirical likelihood approach to the
effective use of auxiliary information in complex surveys”. Statistica
Sinica, 9, pp. 385-406, 1999.
[3] E. Crettaz and C. Suter, ”The impact of Adaptive Preferences on Subjective
Indicators: An Analysis of Poverty Indicators”. Social Indicators
Research, 114, pp. 139-152, 2013.
[4] J.C. Deville and C.E. S¨arndal, ”Calibration estimators in survey sampling”.
Journal of the American Statistical Association, 87, pp. 376-382,
1992.
[5] P. Duchesne, ”Estimation of a proportion with survey data”. Journal of
Statistics Education, 11, pp. 1-24, 2003.
[6] F. Giambona and E. Vassallo, ”Composite Indicator of Social Inclusion
for European Countries”. Social Indicators Research, 116, pp. 269-293,
2014.
[7] D.G. Horvitz and D.J. Thompson, ”A generalization of sampling without
replacement from a finite universe”. Journal of the American Statistical
Association, 47, pp. 663-685, 1952.
[8] R.Lehtonen and A. Veijanen, ”On multinomial logistic generalized
regression estimators”, Survey Methodology, 24, pp. 51-55, 1998.
[9] M. Medeiros, ”The Rich and the Poor: the Construction of an Affluence
Line from the Poverty line”. Social Indicators Research, 78, pp. 1-18,
2006.
[10] I. Molina and J.N.K. Rao, ”Small area estimation of poverty indicators”,
The Canadian Journal of Statistics, 38, pp. 369-385, 2010.
[11] J. Navicke, O. Rastrigina and H. Sutherland, ”Nowcasting Indicators of
Poverty Risk in the European Union: A Microsimulation Approach”.
Social Indicators Research, doi: 10.1007/s11205-013-04918. 2013
[12] J.N.K. Rao, J.G. Kovar and H.J. Mantel, ”On estimating distribution
function and quantiles from survey data using auxiliary information”.
Biometrika, 77, pp. 365-375, 1990
[13] C.E. S¨arndal, B. Swensson and J. Wretman, Model Assisted Survey
sampling, Springer Verlag, 1992.
[14] P.L.D. Silva and C.J. Skinner, ”Estimating distribution function with auxiliary
information using poststratification”. Journal of Official Statistics,
11, pp. 277-294, 1995.
[15] S. Singh, Advanced sampling theory with application: how Michael
selected Amy, Kluver Academic Publisher, 2003.