In this work, we present numerical methods appropriate for parameter estimation in high-dimensional statistical modelling. The solution of these problems is not unique and a crucial question arises regarding the way that a solution can be found. A common choice is to keep the corresponding solution with the minimum norm. There are cases in which this solution is not adequate and regularisation techniques have to be considered. We classify specific cases for which regularisation is required or not. We present a thorough comparison among existing methods for both estimating the coefficients of the model which corresponds to design matrices with correlated covariates and for variable selection for supersaturated designs. An extensive analysis for the properties of design matrices with correlated covariates is given. Numerical results for simulated and real data are presented.

中文翻译：

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解决统计建模中的高维问题：一项比较研究

在这项工作中，我们提出了适用于高维统计建模中参数估计的数值方法。这些问题的解决方案并不是唯一的，一个关键的问题是如何找到解决方案。一个常见的选择是保持相应的解决方案具有最小范数。在某些情况下，这种解决方案是不够的，必须考虑正则化技术。我们对需要或不需要正则化的特定情况进行分类。我们对现有方法进行了彻底的比较，用于估计与具有相关协变量的设计矩阵相对应的模型系数和用于过饱和设计的变量选择。对具有相关协变量的设计矩阵的属性进行了广泛的分析。