变量选择问题是高维数据分析和处理的核心问题之一,特别是近几年,髙维数据的变量选择成为了统计界的研究热点之一。 然而,对于缺失数据下高维数据模型的变量选择问题的研究并不多见。该问题广泛出现在基因数据研究、飞机与炮弹尤其导弹和核弹的测试、医药追踪试验、疾病(特别癌症、艾滋病等疾病)诊断等实际问题中。因此，对该问题的研究具有重要的理论意义和应用价值。.本项目拟研究缺失响应数据下高维半参数分位数回归的变量选择问题。首先系统地研究缺失响应数据下高维稀疏分位数回归估计的统计性质；其次针对不同的惩罚函数建立和完善缺失响应数据下高维数据模型变量选择的分位数回归正则化理论，并开发相应的阈值算法，同时，分析所得选择变量的Oracle性质等。然后将所得理论和算法推广到具有组结构的高维稀疏分位数回归模型；最后研究缺失数据下高维稀疏分位数回归模型变量选择的算法在医药追踪试验、基因数据研究和癌症诊断中的应用。

Variable selection is one of the core issues of high-dimensional data analysis and processing, especially in recent years, variable selection of high dimensional data has become one of the research hot spots of the statistical community. However, variable selection problem of high-dimensional statistical models with missing data is rarely seen yet. The problem occurs in a wide range of genetic data research, aircraft missiles and nuclear bombs and shells especially testing, pharmaceutical tracking test, disease diagnosis (particularly cancer, AIDS and other disease diagnosis) and other practical problems. Therefore, the research on the problem has important theoretical significance and application value. .The project intends to study the variable selection problem on sparse semiparametric quantile regression models with high dimensional data under missing response data. Firstly, a systematical study on the statistical properties of sparse quantile regression estimation in high dimensional statistical models is made under missing response data. Secondly, for different penalty functions,quantile regression regularization theory on variable selection of high dimensional data models are established and improved under missing response data, and corresponding thresholding algorithms are developed, while analyzing the Oracle properties of the resulting select of variables. Then the resulting theory and algorithms are extended to high-dimensional sparse quantile regression model with group structure. Finally，the algorithms on variable selection of high-dimensional sparse quantile regression models under missing data are studied to apply in test track in medicine, genetic data research and cancer diagnosis.