文章摘要
李冬梅,王明秋,王秀丽.基于最小距离法的稳健群组变量选择[J].,2024,64(1):104-110
基于最小距离法的稳健群组变量选择
Robust group variable selection based on minimum distance criterion
  
DOI：10.7511/dllgxb202401013
中文关键词: logistic回归模型  群组变量选择  稳健估计  MM算法
英文关键词: logistic regression model  group variable selection  robust estimation  Majorization-Minimization algorithm
基金项目:国家自然科学基金资助项目(12271294)；山东省自然科学基金资助项目(ZR2020QA021)；全国统计科学研究项目(2022LY071).
作者单位
李冬梅,王明秋,王秀丽  
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中文摘要:
      在研究存在异常值的logistic回归模型时，发现如果使用极大似然估计(MLE)方法进行参数估计，那么异常值引起的偏差不是造成参数估计过大而是导致参数向量内爆即参数向量收缩为零向量，此时如果进行群组变量选择很可能会忽略一些重要变量．因此针对具有组结构的logistic回归模型，为处理解释变量存在异常值时的群组变量选择问题，将基于最小距离法的稳健估计(L2E)方法与已有的3种群组变量选择方法和3种双层变量选择方法结合，在此基础上利用Majorization-Minimization(MM)算法对目标函数进行求解．通过数值模拟比较了基于L2E方法和MLE方法在模型具有组稀疏和双层稀疏的情况下，6种变量选择方法在不同维数下的有限样本表现，结果不仅验证了L2E方法在存在异常值的logistic回归模型参数估计中的稳健性，而且指出了在这6种变量选择方法中使用Group Bridge方法进行变量选择的准确度更高．
英文摘要:
      When studying the logistic regression model with outliers, it is argued that if the maximum likelihood estimation (MLE) method is used for parameter estimation, the deviation caused by the outliers does not cause the parameter estimation to be too large, but causes the parameter vector to implode, that is, the parameter vector shrinks to zero vector. If the group variable selection is performed at this time, some important variables are likely to be ignored. Therefore, for the logistic regression model with group structure and the explanatory variables containing outliers, a robust parameter estimation (L2E) method based on a minimum distance criterion is introduced to combine with the existing three group variable selection methods and three double-layer variable selection methods for variable selection. Majorization-Minimization (MM) algorithm is used to solve the target function. Through numerical simulations, the finite sample performances of the six variable selection methods based on L2E and MLE methods in different dimensions are compared when the model has group sparseness and double-layer sparseness. The results verify that the use of the L2E method for parameter estimation in the logistic regression model with outliers can achieve robustness, and the Group Bridge method is more accurate for variable selection in six variable selection methods.
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