Composing the cumulative quantile regression function and the Goldie concentration curve

Abstract

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.

Concentration curve for truncated and censored data

“…A recent application is the composition of the cumulative quantile regression (CQR) function and the concentration curve as a useful alternative to the CQR function. Tse [14] constructed the strong Gaussian approximation of the associated empirical process. However, data are often taken under restricted conditions.…”