【作者】 汪洋；

【导师】 李周平；

【作者基本信息】 兰州大学 ， 数学， 2023， 硕士

【摘要】 科学技术的进步使得数据的收集越来越便捷,高维数据普遍存在于各个领域,从众多变量中选择出重要的变量成为了统计建模过程中不可或缺的步骤.对于空间数据的变量选择问题,以往的研究侧重于符号一致性或oracle性质,而没有关注变量选择的错误发现率(False discovery rate,FDR).本文在空间线性模型的假定下,提出了能够有效控制FDR的变量选择方法.首先,在误差协方差已知时,本文将knockoff滤波法直接推广到了空间线性模型情形.其次,对于带有条件自回归误差的空间线性模型,提出了knockoff变量的构造条件和数值解法,使用了局部线性近似和最小角回归算法计算参数的惩罚极大似然估计,给出了能够有效控制FDR的变量选择过程.最后,通过数值模拟和实际数据分析验证了本文方法的有效性.理论分析和模拟结果表明,本文提出的变量选择方法能够有效地控制FDR,并且具有较高的选择效率.本研究为空间数据的变量选择问题提供了新的方法和理论支持.更多还原

【Abstract】 The advancement of science and technology has made the collection of data more and more convenient.High-dimensional data generally exists in various fields.Selecting important variables from many variables has become an indispensable step in the process of statistical modeling.For the variable selection of spatial data,previous research only focused on sign consistency or oracle properties,but did not mention the false discovery rate(FDR)of variable selection methods.In this thesis,we develop a variable selection method effectively controling the FDR for spatial linear models.First,the knockoff filtering method is extended to the spatial linear model under the assumption that the error covariance is known.Secondly,for the spatial linear model with conditional autoregressive errors,the construction conditions and numerical solutions of the knockoff variables are proposed,and the penalized maximum likelihood estimator are computed using the local linear approximation and the least angle regression algorithm,giving an effective variable selection procedure to control the FDR.Finally,the validity of the method is verified by numerical simulation and real data analysis.Theoretical analysis and simulation results show that the variable selection method proposed in this thesis can effectively control the FDR while maintaining a high power.This study provides a new method and theoretical support for the variable selection of sptial data analysis.更多还原