Estimating the Lorenz curve and Gini index with right censored data: a Polya tree approach

Blum, J., Susarla, V.: On the posterior distribution of a Dirichlet process given randomly right censored observations. Stoch. Process. Appl. 5, 207–211 (1977)

Burkhauser, R.V., Feng, S., Jenkins, S., Larrimore, J.: Estimating trends in US income inequality using the Current Population Survey: the importance of controlling for censoring. J. Econ. Inequal. 9, 393–415 (2011)

Chotikapanich, D., Griffiths, W.: Estimating Lorenz curves using Dirichlet distribution. J. Bus. Econ. Stat. 20, 290–295 (2002)

Cowell, F., Flaichaire, E.: Income distribution and inequality measurement: the problem of extreme values. J. Econom. 141, 1044–1072 (2007)

Cowell, F., Victoria Feser, M.P.: Statistical inference for Lorenz curves with censored data. Discussion Paper No. DARP/35 (1998)

Cowell, F., Victoria-Feser, M.P.: Distributional dominance with trimmed data. J. Bus. Econ. Stat. 24, 291–300 (2006)

De Finetti, B.: Il problema della perequazione. In: Atti della Società Italiana per il Progresso delle Scienze, (XII Riunione), Napoli (1935)

Doksum, K.A.: Tailfree and neutral random probabilities and their posterior distributions. Ann. Probab. 2, 183–201 (1974)

Fabius, J.: Asymptotic behavior of Bayes estimate. Ann. Math. Stat. 35, 846–856 (1964)

Ferguson, T.S.: A Bayesian analysis on some nonparametric problems. Ann. Stat. 1, 209–230 (1973)

Ferguson, T.S.: Prior distributions on spaces of probability measures. Ann. Stat. 2, 615–629 (1974)

Fienberg, S.E., Steele, R.J., Makov, U.E.: Statistical notion of data disclosure avoidance and their relationship to traditional statistical methodology: data swapping and loglinear models. In: Proceedings of the Bureau of the Census 12th Annual Research Conference, pp. 87–105 (1996)

Freedman, D.A.: On the asymptotic behavior of Bayes’ estimate in the discrete case. Ann. Math. Stat. 34, 1386–1403 (1963)

Gastwirth, J.L.: A general definition of the Lorenz curve. Econometrica 31, 1037–1039 (1971)

George, E.I., Hui, S.K.: Optimal pricing using online auction experiments: a Polya tree approach. Ann. Appl. Stat. 6, 55–82 (2012)

Ghosh, J.K., Ramamoorthi, R.V.: Bayesian Nonparametrics. Springer, New York (2003)

Gini, C.: Variabilità e mutabilità. In: Contributo allo studio delle distribuzioni e relazioni statistiche. Studi Economico-Giuridici dell’Università di Cagliari III (1912)

Gini, C.: Sulla misura della concentrazione e della Variabilità dei caratteri. In: Atti del Reale Istituto Veneto di Scienze, Lettere ed Arti LXXIII(part 2), pp. 1203–1248 (1914)

Gottschak, P., Smeeding, T.M.: Empirical evidence in income inequality in industrialized countries. In: Atkinson, A., Bourguignon, F. (eds.) Handbook of Income Distribution, Chap. 3. North-Holland, Amsterdam

Hanson, T., Johnson, W.O.: Modeling regression error with a mixture of Polya trees. J. Am. Stat. Assoc. 101, 1548–1565 (2002)

Hasegawa, H., Kozumi, H.: Estimation of Lorenz curves: a Bayesian nonparametric approach. J. Econ. 115, 277–291 (2003)

Kendall, M., Stuart, A.: The Advanced Theory of Statistics. Mac Millan Publishing, New York (1977)

Lavine, M.: Some aspects of Polya tree distributions for statistical modelling. Ann. Stat. 20, 1222–1235 (1992)

Lavine, M.: More aspects of Polya tree distributions for statistical modelling. Ann. Stat. 22, 1161–1176 (1994)

Lorenz, M.O.: Methods of measuring the concentration of wealth. Publ. Am. Stat. Assoc. 9, 209–219 (1905)

Mauldin, D., Sudderth, W.D., Williams, S.C.: Polya trees and random distributions. Ann. Stat. 20, 1203–1221 (1992)

Müller, P., Quintana, F.: More nonparametric Bayesian models for biostatistics. In: Hjort, N.L., Holmes, C., Müller, P., Walker, S.G. (eds.) Bayesian Nonparametrics. Cambridge University Press, Cambridge (2010)

Muliere, P., Walker, S.: A Bayesian non-parametric approach to survival analysis using Polya trees. Scand. J. Stat. 24, 331–340 (1997)

Neath, A.A.: Polya tree distributions for statistical modeling of censored data. J. Appl. Math. Decis. Sci. 7, 175–186 (2003)

Nieto-Barajas, L.E., Müller, P.: Rubbery Polya tree. Scand. J. Stat. 39, 166–184 (2012)

Pietra, G.: Delle relazioni tra gli indici di Variabilità, I, pp. 775–804. II. Atti del Reale Istituto Veneto di Scienze, Lettere ed Arti LXXIV(II) (1915)

Robert, C.P., Casella, G.: Monte Carlo Statistical Methods, 2nd edn. Springer, New York (2004)

Susarla, V., Van Ryzin, J.: Non parametric Bayesian estimation of survival curves from incomplete observations. J. Am. Stat. Assoc. 71, 897–902 (1976)

Van Kerm, P.: Extreme incomes and the estimation of poverty and inequality indicators from EU-SILC. IRISS Working Paper Series 2007–01, CEPS/INSTEAD, Differdange, Luxembourg (2007)

Walker, S., Mallick, B.: Hierarchical generalized linear models and frailty models with Bayesian nonparametric mixing. J. R. Stat. Soc. Ser. B 59, 845–860 (1997)