Quantile Regression, as introduced by Koenker, R. and Bassett, G. (1978), provides a complete picture of the relationship between the response variable and covariates by estimating a family of conditional quantile functions. Also, it offers a natural solution to challenges such as; homoscedasticity and sometimes unrealistic normality assumption in the usual conditional mean regression. Most of the results for quantile regression are based on simple random sampling (SRS). In this thesis, we study the quantile regression with rank-based sampling methods. Rank-based sampling methods have a wide range of applications in medical, ecological and environmental research, and have been shown to perform better than SRS in estimating several population parameters. We propose a new objective function which takes into account the ranking information to estimate the unknown model parameters based on the maxima or minima nomination sampling designs. We compare the mean squared error of the proposed quantile regression estimates using maxima (or minima) nomination sampling design and observe that it provides higher relative e ciency when compared with its counterparts under SRS design for analyzing the upper (or lower) tails of the distribution of the response variable. We also evaluate the performance of our proposed methods when ranking is done with error. / February 2017