Estimation of a precision matrix (i.e. inverse covariance matrix) is widely used to exploit conditional independence among continuous variables. The influence of abnormal observations is exacerbated in a high dimensional setting as the dimensionality increases. In this work, we propose robust estimation of the inverse covariance matrix based on an $l_1$ regularised objective function with a weighted sample covariance matrix. The robustness of the proposed objective function can be justified by a nonparametric technique of the integrated squared error criterion. To address the non-convexity of the objective function, we develop an efficient algorithm in a similar spirit of majorisation-minimisation. Asymptotic consistency of the proposed estimator is also established. The performance of the proposed method is compared with several existing approaches via numerical simulations. We further demonstrate the merits of the proposed method with application in genetic network inference.

精度矩阵（即逆协方差矩阵）的估计被广泛用于开发连续变量之间的条件独立性。随着维数的增加，异常观察的影响在高维设置中会加剧。在这项工作中，我们提出了基于逆协方差矩阵的稳健估计${升}_1$具有加权样本协方差矩阵的正则化目标函数。所提出的目标函数的鲁棒性可以通过积分平方误差准则的非参数技术来证明。为了解决目标函数的非凸性问题，我们本着类似的优化-最小化的精神开发了一种有效的算法。还建立了建议的估计量的渐近一致性。通过数值模拟将所提出方法的性能与几种现有方法进行了比较。我们进一步证明了所提出方法在遗传网络推理中的应用的优点。