分位数回归中若干统计问题及其在气候变化和水文模型中的应用

Quantile regression is one of tools which are used to investigate climate change and hydrological data. When using it to analyze climate change and hydrological data, some issues may be happen: crossing of parameter estimators at different quantile points and invalidation of the existing estimating methods, especially under finite sample size. These issues may give rise to some difficulty to analyze and explain climate change and hydrological data. In this project，we would make a plan to propose a new non-crossing estimating method to get a non-crossing estimator under the quantile regression model and investigate its theoretical property. This new non-crossing method could conquer the crossing problem of parameter estimators at different quantile points. Further, we would design a new quantile regression model based on the background of climate change and hydrological data. Under this new model, we would propose a new estimating method, named extrapolation, to obtain a quantile estimating curve, and investigate its theoretical property. This curve could provide a definite and valid estimator at any quantile point，including all upper and lower quantile points. After completing this theoretical research, we would use our new-proposed methods to analyze climate change and hydrological data, explain and predict the impact of climate change on the environment.

分位数回归模型是分析研究气候和水文数据的重要统计工具之一。 用它分析气候和水文数据时，会出现以下问题：(1)在不同分位点的估计会出现交叉，这为合理解释气候和水文数据带来了困难；(2)用现有的估计方法去分析气候和水文数据时，在极高或极低的分位点，这些方法可能会失效，尤其是在小样本量下。基于以上两个问题，本项目的研究主要集中在以下几个方面：(1)拟提出分位数回归模型下的非交叉估计，并研究这个估计的大样本性质以及相关的假设检验问题；(2)拟引进一个参数项是函数的分位数回归模型，用外推法来估计新模型中参数和分位数曲线，研究参数估计和分位数曲线估计的大样本性质，新的估计方法永远不会失效；(3)完成了理论和方法研究后，拟用新提出的两类估计方法分析手头有的气候和水文数据，解决用现有方法去分析时存在的问题（估计的交叉性和失效性），以便能更好地解释这些数据。