Abstract
M-quantile small area estimation (SAE) methods constitute a set of advanced statistical inference techniques that can be used for the measurement of poverty and living conditions by survey practitioners, researchers in private and public organizations, official statistical agencies, and local governmental agencies. In particular, the estimates produced using these SAE methods are well suited to mapping geographical variations in these conditions. In this paper, we summarize the ideas set out in some recent papers on M-quantile methods and their extensions and also comment on important issues that arise when SAE methods are used in poverty assessment in three Italian Regions.
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Notes
- 1.
As a remark, it is important to underline that EU-SILC and census data are confidential. These data were provided by ISTAT, the Italian National Institute of Statistics, to the researchers of the SAMPLE project and were analyzed for the present analysis respecting all confidentiality restrictions.
- 2.
This is computed as the Disposable Household Income multiplied by the Within-household non-response inflation factor and divided by the equivalized household size (EHS). The Disposable Household Income is the sum for all household members of gross personal income components plus gross income components at household level minus employer’s social insurance contributions, interest paid on mortgage, regular taxes on wealth, regular inter-household cash transfer paid, tax on income, and social insurance contributions. The Within-household non-response inflation factor is the factor by which it is necessary to multiply the total gross income, the total disposable income, or the total disposable income before social transfers to compensate the non-response in individual questionnaires. The EHS is obtained as \(\mathrm{EHS} = 1 + 0.5 \cdot (\mathrm{HM}_{14+} - 1) + 0.3 \cdot \mathrm{HM}_{13-}\), where HM14+ is the number of household members aged 14 and over (at the end of income reference period), HM13− be the number of household members aged 13 or less (at the end of income reference period). By this way we take into account the economy of scale present in an household (Eurostat 2007).
References
Brandolini, A., Saraceno, C.: Introduzione. In: Brandolini, A., Saraceno, C. (eds.) Povertá e Benessere. Una geografia delle disuguaglianze in Italia. Il Mulino, Bologna (2007)
Brunsdon, C., Fotheringham, A.S., Charlton, M.: Geographically weighted regression: a method for exploring spatial nonstationarity. Geographical Anal. 28, 281–298 (1996)
Chambers, R.L., Dunstan, R.: Estimating distribution functions from survey data. Biometrika 73, 597–604 (1996)
Chambers, R.L., Pratesi, M.: Small area methodology in poverty mapping: An introductory overview. In: Lemmi, A., Betti, G. (eds.) Poverty and Social Exclusion: New Methods of Analysis. Routledge, London (2013)
Chambers, R.L., Tzavidis, N.: M-quantile models for small area estimation. Biometrika 93, 255–268 (2006)
Chambers, R.L., Chandra, H., Tzavidis, N.: On bias robust mean squared error estimation for pseudolinear small area estimators. Surv. Methodol. 37(2), 153–170 (2011)
Chambers, R.L., Chandra, H., Salvati, N., Tzavidis, N.: Outliers robust small area estimation. J. R. Stat. Soc. B 76, 47–69 Part 1 (2014)
Cheli, B., Lemmi, A.: A totally fuzzy and relative approach to the multidimensional analysis of poverty. Econ. Notes 24, 115–134 (1995)
Elbers, C., Lanjouw, J.O., Lanjouw, P.: Micro-level estimation of poverty and inequality. Econometrica 71, 355–364 (2003)
Eurostat: Description of SILC user database variables. Version 2007.1 from 01-03-2009. Eurostat (2007)
Fabrizi, E., Salvati, N., Pratesi, M.: Constrained small area estimators based on M-quantile methods. J. Off. Stat. 28(1), 89–106 (2012)
Fabrizi, E., Salvati, N., Pratesi, M., Tzavidis, N.: Outlier robust model-assisted small area estimation. Biom. J. 56(1), 157–175 (2014)
Foster, J., Greer, J., Thorbecke, E.: A class of decomposable poverty measures. Econometrica 52, 761–766 (1984)
Giusti, C., Pratesi, M., Salvati, N.: Small area methods in the estimation of poverty indicators: The case of Tuscany. Polit. Econ. 3, 369–380 (2009)
Giusti, C., Tzavidis, N., Pratesi, M., Salvati, N.: Resistance to outliers of M-quantile and robust random effects small area models. S3RI Methodology Working Papers M11/04. Southampton Statistical Sciences Research Institute, University of Southampton (2011)
ISTAT: L’indagine europea sui redditi e le condizioni di vita delle famiglie (Eu-Silc). Metodi e Norme 37, 1–191 (2008)
Marchetti, S., Tzavidis, N., Pratesi, M.: Nonparametric bootstrap mean squared error estimation for M-quantile estimators for small area averages, quantiles and poverty indicators. Comput. Stat. Data Anal. 56, 2889–2902 (2012)
Molina, I., Rao, J.N.K.: Small area estimation of poverty indicators. Can. J. Stat. 38, 369–385 (2010)
Petrucci, A., Salvati, N.: Small area estimation for spatial correlation in watershed erosion assessment. J. Agric. Biol. Environ. Stat. 11, 169–182 (2006)
Pratesi, M., Salvati, N.: Small area estimation: the EBLUP estimator based on spatially correlated random area effects. Stat. Methods Appl. 17, 113–141 (2008)
Pratesi, M., Salvati, N.: Small area estimation in the presence of correlated random area effects. J. Off. Stat. 25, 37–53 (2009)
Pratesi, M., Ranalli, M.G., Salvati, N.: Semiparametric M-quantile regression using penalized splines. J. Nonparametr. Stat. 21, 287–304 (2008a)
Pratesi, M., Ranalli, M.G., Salvati, N.: Semiparametric M-quantile regression for estimating the proportion of acidic lakes in 8-digit HUCs of the North-eastern US. Environmetrics 19, 687–701 (2008b)
Pratesi, M., Giusti, C., Salvati, N.: Estimation of poverty indicators in Italy: A small area M-quantile based approach. Riv. Ital. Econ. Demogr. Stat. LXIII(1–2), 243–256 (2009)
Pratesi, M., Giusti, C., Marchetti, S., Salvati, N., Tzavidis, N., Molina, I., Durbán, M., Grané, A., Marín, J.M., Veiga, M.H., Morales, D., Esteban, M.D., Sánchez, A., Santamaría, L., Marhuenda, Y., Pérez, A., Pagliarella, M.C., Rao, J.N.K., Ferretti, C.: Sample deliverables 12 and 16. Final small area estimation developments and simulations results. Available at http://www.sample-project.eu/it/the-project/deliverables-docs.html (2010)
Pratesi, M., Giusti, C., Marchetti, S., Salvati, N.: Robust small area estimation of poverty indicators. In: Survey Research Methods and Applications. Edizioni Plus, Pisa (2011)
Pratesi, M., Marchetti, S., Giusti, C.: Small area estimation of poverty indicators. In: Davino, C., Fabbris, L. (eds.) Survey Data Collection and Integration. Springer, New York (2013)
Rao, J.N.K.: Small Area Estimation. Wiley, New York (2003)
Salvati, N., Ranalli, M.G., Pratesi, M.: Small area estimation of the mean using nonparametric M-quantile regression: A comparison when a linear mixed model does not hold. J. Stat. Comput. Simul. 81(8), 945–964 (2011)
Salvati, N., Tzavidis, N., Pratesi, M., Chambers, R.: Small area estimation via M-quantile geographically weighted regression. TEST 21(1), 1–28 (2012)
Salvati, N., Giusti, C., Pratesi, M.: The use of spatial information for the estimation of poverty indicators at the small area level. In: Lemmi, Betti (eds.) Poverty and Social Exclusion: New Methods of Analysis. Routledge, London (2013)
Sinha, S.K., Rao, J.N.K.: Robust small area estimation. Can. J. Stat. 37, 381–399 (2009)
Tzavidis, N., Salvati, N., Pratesi, M., Chambers, R.: M-quantile models with application to poverty mapping. Stat. Methods Appl. 17(3), 393–411 (2008)
Tzavidis, N., Marchetti, S., Chambers, R.: Robust prediction of small area means and distributions. Aust. N. Z. J. Stat. 52, 167–186 (2010)
Acknowledgements
This work was financially supported by the European Project SAMPLE “Small Area Methods for Poverty and Living Condition Estimates,” European Commission 7th FP—www.sample-project.eu. My personal thanks to Caterina Giusti, Stefano Marchetti, and Nicola Salvati for their assistance and contributions.
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Pratesi, M. (2014). M-Quantile Small Area Models for Measuring Poverty at a Local Level. In: Mecatti, F., Conti, P., Ranalli, M. (eds) Contributions to Sampling Statistics. Contributions to Statistics. Springer, Cham. https://doi.org/10.1007/978-3-319-05320-2_2
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