Quantile regression and the duration of unemployment

Powell (1986) proposed a quantile regression estimator for censored regression models on the basis of equivariance of quantiles to monotone transformations. In this thesis, censored quantile regression models are generalized using two-parameter Box-Cox transformation to relax the conventional linear specification of functional form, and the quantile regression estimator of the parameters of the transformed and censored regression models is presented. Both the $N\sp{1/2}$-consistency and the asymptotic normality of quantile estimator are derived for nonlinear regression models. The proof of asymptotic normality is based on the approach introduced by Pollard (1989) using maximal inequalities and quadratic approximation to the objective function, thus simplifying the argument and relaxing the need for convexity of the objective function in the parameter vector.