On Estimating the Headcount Index by Using the Logistic Regression Estimator
The problem of estimating a proportion has important
applications in the field of economics, and in general, in many areas
such as social sciences. A common application in economics is
the estimation of the headcount index. In this paper, we define the
general headcount index as a proportion. Furthermore, we introduce
a new quantitative method for estimating the headcount index. In
particular, we suggest to use the logistic regression estimator for the
problem of estimating the headcount index. Assuming a real data set,
results derived from Monte Carlo simulation studies indicate that the
logistic regression estimator can be more accurate than the traditional
estimator of the headcount index.
[1] Y.G. Berger and C.J. Skinner, "Variance estimation for a low income
proportion”. Journal of the Royal Statistical Society, Series B, 52, pp.
457–468 2003.
[2] C.R. Blyth and H.A. Still, "Binomial confidence intervals”. Journal of
the American Statistical Association, 78, pp. 108–116, 1983.
[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] F. Giambona, F. and E. Vassallo, ”Composite Indicator of Social
Inclusion for European Countries”. Social Indicators Research, 116, pp.
269-293, 2014.
[5] R.Lehtonen and A. Veijanen, ”On multinomial logistic generalized
regression estimators”, Survey Methodology, 24, pp. 51-55, 1998.
[6] 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.
[7] I. Molina and J.N.K. Rao, ”Small area estimation of poverty indicators”,
The Canadian Journal of Statistics, 38, pp. 369-385, 2010.
[8] J.F. Mun˜oz, E. A´ lvarez, A. Arcos, M.M. Rueda, S. Gonza´lez and A.
Santiago, "Optimum ratio estimators for the population proportion”,
International Journal of Computer Mathematics, 89, pp. 357-365, 2012.
[9] R.G. Newcombe, "Two-sided confidence intervals for the single proportion:
comparison of seven methods”. Statistic in Medicine, 17, pp.
857–872, 1998.
[10] M.M. Rueda, J.F. Mun˜oz, A. Arcos, E. A´ lvarez and S. Mart´ınez, "Estimators
and confidence intervals for the proportion using binary auxiliary
information with application to pharmaceutical studies”. Journal of
Biopharmaceutical Statistics, 21, pp. 526–554, 2011.
[11] M.M. Rueda, J.F. Mun˜oz, A. Arcos and E. A´ lvarez, "Indirect estimation
of proportions in natural resource surveys”. Mathematics and Computers
in Simulation, 81, pp. 2317–2325, 2011.
[12] C.E. S¨arndal, B. Swensson and J. Wretman, Model Assisted Survey
sampling, Springer Verlag, 1992.
[13] S.E. Vollset, "Confidence interval for a binomial proportion”. Statistic
in Medicine, 12, pp. 809–824, 1993.
[14] E.B. Wilson, "Probable inference, the law of succession, and statistical
inference”. Journal of the American Statisitical Association, 22, pp. 209–
212, 1927
[1] Y.G. Berger and C.J. Skinner, "Variance estimation for a low income
proportion”. Journal of the Royal Statistical Society, Series B, 52, pp.
457–468 2003.
[2] C.R. Blyth and H.A. Still, "Binomial confidence intervals”. Journal of
the American Statistical Association, 78, pp. 108–116, 1983.
[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] F. Giambona, F. and E. Vassallo, ”Composite Indicator of Social
Inclusion for European Countries”. Social Indicators Research, 116, pp.
269-293, 2014.
[5] R.Lehtonen and A. Veijanen, ”On multinomial logistic generalized
regression estimators”, Survey Methodology, 24, pp. 51-55, 1998.
[6] 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.
[7] I. Molina and J.N.K. Rao, ”Small area estimation of poverty indicators”,
The Canadian Journal of Statistics, 38, pp. 369-385, 2010.
[8] J.F. Mun˜oz, E. A´ lvarez, A. Arcos, M.M. Rueda, S. Gonza´lez and A.
Santiago, "Optimum ratio estimators for the population proportion”,
International Journal of Computer Mathematics, 89, pp. 357-365, 2012.
[9] R.G. Newcombe, "Two-sided confidence intervals for the single proportion:
comparison of seven methods”. Statistic in Medicine, 17, pp.
857–872, 1998.
[10] M.M. Rueda, J.F. Mun˜oz, A. Arcos, E. A´ lvarez and S. Mart´ınez, "Estimators
and confidence intervals for the proportion using binary auxiliary
information with application to pharmaceutical studies”. Journal of
Biopharmaceutical Statistics, 21, pp. 526–554, 2011.
[11] M.M. Rueda, J.F. Mun˜oz, A. Arcos and E. A´ lvarez, "Indirect estimation
of proportions in natural resource surveys”. Mathematics and Computers
in Simulation, 81, pp. 2317–2325, 2011.
[12] C.E. S¨arndal, B. Swensson and J. Wretman, Model Assisted Survey
sampling, Springer Verlag, 1992.
[13] S.E. Vollset, "Confidence interval for a binomial proportion”. Statistic
in Medicine, 12, pp. 809–824, 1993.
[14] E.B. Wilson, "Probable inference, the law of succession, and statistical
inference”. Journal of the American Statisitical Association, 22, pp. 209–
212, 1927
@article{"International Journal of Engineering, Mathematical and Physical Sciences:67345", author = "Encarnación Álvarez and Rosa M. García-Fernández and Juan F. Muñoz and Francisco J. Blanco-Encomienda", title = "On Estimating the Headcount Index by Using the Logistic Regression Estimator", abstract = "The problem of estimating a proportion has important
applications in the field of economics, and in general, in many areas
such as social sciences. A common application in economics is
the estimation of the headcount index. In this paper, we define the
general headcount index as a proportion. Furthermore, we introduce
a new quantitative method for estimating the headcount index. In
particular, we suggest to use the logistic regression estimator for the
problem of estimating the headcount index. Assuming a real data set,
results derived from Monte Carlo simulation studies indicate that the
logistic regression estimator can be more accurate than the traditional
estimator of the headcount index.
", keywords = "Poverty line, poor, risk of poverty, sample, Monte
Carlo simulations.", volume = "8", number = "8", pages = "1126-3", }
