In the paper conditional inequality curves and measures are proposed which allow us to describe the inequality/concentration of the conditional distribution of the feature we are interested in with respect to certain continuous variables. Moreover, for a graphical illustration of the change in values of the proposed conditional indices, a curve of conditional inequality measures is introduced. To estimate the curves and measures, a new method is proposed to estimate the conditional quantile function. This method uses quantile regression estimates for a given set of quantile orders, followed by isotonic regression on the estimated regression coefficients to ensure that the estimated conditional quantile function is nondecreasing. The consistency of the proposed estimators is proved while their finite sample performance is evaluated through simulation studies and compared with existing approaches. Finally, practical application of conditional curves and measures is demonstrated by determining estimated curves of conditional salary inequalities with respect to years of experience in different employee tenure groups, based on some real data. The code used to prepare the simulation results presented in this paper is available in a dedicated GitHub repository.

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