Saddlepoint approximations for the distribution of regression quantiles
Since their introduction in 1978, regression quantiles have played an increasingly important role in regression analysis. In particular, they form the basis for quantile regression, a statistical technique intended to draw inferences about conditional quantile functions. Although it is well known that regression quantiles have limiting normal distributions, not much is known about their behaviour in finite and small samples. In the present paper we study this problem and, in particular, apply the saddlepoint method to obtain improved small sample approximations. These approximations are considered in a numerical study where they are found to perform quite well even in fairly small samples.