Quantile Regression with Left-Truncated and Right-Censored Data in a Reproducing Kernel Hilbert Space

Li et al. (2007) developed an estimation method for quantile functions in a reproducing kernel Hilbert space for complete data, and Park and Kim (2011)proposed an estimation method using the epsilon-insensitive loss. This article extends these estimation methods to left-truncated and right-censored data. As a measure of goodness of fit, the check loss and the epsilon-insensitive loss were used to estimate the quantile function. The epsilon-insensitive loss can shrink the estimated coefficients toward zero; hence, it can reduce the variability of the estimates. Simulation studies show that the estimated quantile functions based on the epsilon-insensitive loss perform slightly better when c is adequately chosen.