Conditional Quantile for Truncated Dependent data

Abstract

In this thesis we study some asymptotic properties of the kernel conditional quantile estimator when the interest variable is subject to random left truncation. The uniform strong convergence rate of the estimator is obtained. In addition, it is shown that, under regularity conditions and suitably normalized, the kernel estimate of the conditional quantile is asymptotically normally distributed. Our interest in conditional quantile estimation is motivated by it's robusteness, the constructing of the confidence bands and the forecasting from time series data. Our results are obtained in a more general setting (strong mixing) which includes time series modelling as a special case .