There is a growing demand for multivariate economic statistics for crossclassified domains. In business statistics, this demand poses a particular challenge given the specific character of the population of enterprises, which necessitates searching for methods of analysis that would represent the robust approach to estimation, where auxiliary variables could be utilised. The adoption of new solutions in this area is expected to increase the scope of statistical output and improve the precision of estimates. The study presented in the paper furthers this goal, as it is focused on testing the application of a robust version of the Fay-Herriot model, which makes it possible to meet the assumption of normality of random effects under the presence of outliers. These alternative models are supplied to estimate the parameters of small firms operating in 2012. Variables from administrative registers were used as auxiliary variables, which made the estimation process more comprehensive. The paper refers to small area estimation methods. The variables of interest are estimated at a low level of aggregation represented by the crosssection province and NACE sections.
robust estimation, business statistics, small area estimation, Fay-Herriot model
C40, C13, C40, C51, M20
Boonstra H. J., Buelens B., (2011), Model-based estimation, Statistics Netherlands, Hague, Heerlen.
Dehnel G., (2017), GREG estimation with reciprocal transformation for a Polish business survey [in:] Papież M., Śmiech S. (eds.) The 11th Professor Aleksander Zelias Internetional Conference on Modelling and Forecasting of Socio-Economic Phenomena. Conference Proceedings, Foundation of the Cracow University of Economics, Cracow, 67–75.
Dehnel G., Pietrzak M., Wawrowski Ł., (2017), Estymacja przychodu przedsiębiorstw na podstawie modelu Faya-Herriota, Przegląd Statystyczny, 64(1), 79–94.
Dehnel G., Wawrowski Ł., (2018), Robust estimation of revenues of Polish small companies by NACE section and province, [in:] Papież M., Śmiech S. (eds.), Proceedings of the 12th Professor Aleksander Zelias International Conference on Modelling and Forecasting of Socio-Economic Phenomena, Foundation of the Cracow University of Economics, Cracow, 110–119.
Eurostat (2013), Handbook on precision requirements and variance estimation for ESS households surveys, European Union, Luxembourg.
Fay R. E., Herriot R. A., (1979), Estimates of income for small places: an application of James-Stein procedures to census data, Journal of the American Statistical Association, 74(366a), 269–277.
González-Manteiga W., Lombardia M. J., Molina I., Morales D., Santamaría L., (2008), Bootstrap mean squared error of a small-area EBLUP, Journal of Statistical Computation and Simulation, 78(5), 443–462.
GUS (2013), Ludność. Stan i struktura demograficzno-społeczna. Narodowy Spis Powszechny Ludności i Mieszkań 2011, GUS, Zakład Wydawnictw Statystycznych, Warszawa.
GUS (2017), Działalność przedsiębiorstw niefinansowych w 2015 roku, GUS, Warszawa.
Horvitz D. G., Thompson D. J., (1952), A generalization of sampling without replacement from a finite universe, Journal of the American statistical Association, 47(260), 663–685.
Huber P. J., (1981), Robust Statistics, John Wiley and Sons, New York.
Krzciuk, M. (2017). On the Simulation Study of Jackknife and Bootstrap MSE Estimators of a Domain Mean Predictor for Fay-Herriot Model. Acta Universitatis Lodziensis. Folia Oeconomica, 5(331), 169-183.
Rao J. N. K., (2014), Small-Area Estimation, John Wiley & Sons, Hoboken, New Yersey.
Sinha S. K., Rao J. N. K., (2009), Robust small area estimation, Canadian Journal of Statistics, 37(3), 381–399.
Warnholz S., (2016), Small Area Estimation Using Robust Extensions to Area Level Models, (doctoral dissertation), Freie Universität, Berlin.
Żądło T., (2008), Elementy statystyki małych obszarów z programem R, Wydawnictwo Akademii Ekonomicznej im. Karola Adamieckiego, Katowice.
Żądło T., (2012), O predykcji wartości globalnej w domenie z wykorzystaniem informacji o zmiennych dodatkowych przy założeniu modelu Faya-Herriota, Acta Universitatis Lodziensis. Folia Oeconomica, 271, 243–256.