应用核估计、局部多项式估计、参数与非参数方法、经验似然、惩罚与惩罚经验似然等技术以及综合应用其中的方法，包括创新一些更有效的推断方法，研究分位数回归模型的估计与模型测试问题，其中研究的模型包括参数模型、非参数及半参数单指标模型、变系数模型、协整模型等；观察到的数据包括完全数据和右删失、左截断、既左截断同时又右删失、随机丢失、以及既随机右删失同时发生随机丢失等不完全数据，平稳与非平稳时间序列，高维数据，各种相依数据等；研究的问题包括非参数分位数回归估计、模型中参数与非参数函数的估计、模型的变量选择、模型的变点分析等；研究结论围绕估计量的相合性、渐近正态性、似然统计量和检验统计量的渐近分布、估计量过程的弱收敛性，一致收敛速度及积分收敛速度等。利用实际数据和模拟数据对理论结果做模拟验证，并探索理论结果在实际问题中的应用。

By applying the estimate methods of kernel,local polynomial,parametric and non-paramentric,empirical likelihood,penalized empirical likelihood as well as their synthesis,which include some more effective methods of inference,we study the estimation and test of the quantile regression model.The investigated models include the parametric model,non-paramentric and semi-parametric single index model,varying-coefficient model,cointegrating regression,and so on.The observed data include the imcomplete data,which relate to the right censoring,left truncation,both left truncation and right censoring,missing at random,and random right censoring with missing at random,stationary and non-stationary time series,high-dimensional data,various dependent data,and so on.The studied problems include the non-parametric quantile regression estimation,estimation of the parametric and non-parametric functions in the models,variable selection and change point analysis of the models,and so on.The studied conclusions relate to the consistency and asymptotic normality of the proposed estimators;asymptotic distribution of the likelihood statistic and test statistic;the weak convergence,convergence rate and Integral convergence rate of the process for estimators,and so on.Simulation study and real data analysis are done to evaluate the performance of the proposed methods.Applications in practical problems based on the obtained theoretical results are explored.