Lorenz Curve for Truncated and Censored Data

Tse, SzeMan

doi:10.1007/s10463-006-0039-7

Cited by 11 publications

(12 citation statements)

References 16 publications

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“…Csörgő and Zitikis [4,5] proved a more general version of the LIL under weaker assumptions, and in [6] they constructed confidence bands for the Lorenz and Goldie curves. Tse [17] established the corresponding results for censored and truncated data.…”

Section: Introductionmentioning

confidence: 96%

Composing the cumulative quantile regression function and the Goldie concentration curve

Tse

2011

Journal of Multivariate Analysis

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a b s t r a c tThe model we discuss in this paper deals with inequality in distribution in the presence of a covariate. To elucidate that dependence, we propose to consider the composition of the cumulative quantile regression (CQR) function and the Goldie concentration curve, the standardized counterpart of which gives a fraction to fraction plot of the response and the covariate. It has the merit of enhancing the visibility of inequality in distribution when the latter is present. We shall examine the asymptotic properties of the corresponding empirical estimator. The associated empirical process involves a randomly stopped partial sum process of induced order statistics. Strong Gaussian approximations of the processes are constructed. The result forms the basis for the asymptotic theory of functional statistics based on these processes.

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Section: Introductionmentioning

confidence: 96%

Composing the cumulative quantile regression function and the Goldie concentration curve

Tse

2011

Journal of Multivariate Analysis

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“…Consider the unemployment duration data and trade duration data, the censoring occurs when individuals are still unemployed or when the trade relationships continue to evolve at the time of the interview. Recently, researchers studied the Gini estimation with censored data (Tse 2006;Bonetti et al 2009;Gigliarano and Muliere 2013). Tse (2006) and Bonetti et al (2009) considered Gini estimation under independent censoring, that is,T i ⊥C i .…”

Section: Introductionmentioning

confidence: 99%

“…Recently, researchers studied the Gini estimation with censored data (Tse 2006;Bonetti et al 2009;Gigliarano and Muliere 2013). Tse (2006) and Bonetti et al (2009) considered Gini estimation under independent censoring, that is,T i ⊥C i . Gigliarano and Muliere (2013) required prior distribution information.…”

Section: Introductionmentioning

confidence: 99%

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Gini index estimation for lifetime data

Zhang

Guang-yu

2016

Lifetime Data Anal

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Lifetime data is often right-censored. Recent literature on the Gini index estimation with censored data focuses on independent censoring. However, the censoring mechanism is likely to be dependent censoring in practice. This paper proposes two estimators of the Gini index under independent censoring and covariate-dependent censoring, respectively. The proposed estimators are consistent and asymptotically normal. We also evaluate the performance of our estimators in finite samples through Monte Carlo simulations. Finally, the proposed methods are applied to real data.

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“…The properties of the PL-Lorenz curve have been examined by Tse [13]. We aim to accomplish the same for the PL-concentration curve in this paper.…”

Section: Introductionmentioning

confidence: 99%

Concentration curve for truncated and censored data

Tze

2014

Math. Meth. Stat.

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Concentration curve is the inverse Lorenz curve. Together, they form the basis for most measures of distributional inequality. In this paper, we consider the empirical estimator of the concentration curve when the data are subjected to random left truncation and/or right censorship. Simultaneous strong Gaussian approximations for the associated Lorenz and normed concentration processes are established under appropriate assumptions. Functional laws of the iterated logarithm for the two processes are established as easy consequences. The construction provides a solid foundation for the study of functional statistics based on the two processes.

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Lorenz Curve for Truncated and Censored Data

Abstract: Left truncatrion, Right censorship, Product-limit, Quantile process, Strong Gaussian approximations, Lorenz process, Gini index, Law of the iterated logarithm,

Cited by 11 publications

References 16 publications

Composing the cumulative quantile regression function and the Goldie concentration curve

Composing the cumulative quantile regression function and the Goldie concentration curve

Gini index estimation for lifetime data

Concentration curve for truncated and censored data

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