**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**33030

##### On Estimating the Headcount Index by Using the Logistic Regression Estimator

**Authors:**
Encarnación Álvarez,
Rosa M. García-Fernández,
Juan F. Muñoz,
Francisco J. Blanco-Encomienda

**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.

**Digital Object Identifier (DOI):**
doi.org/10.5281/zenodo.1094357

**References:**

[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