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In this article, we consider the problem of estimating the precision matrix when the sample data contains cellwise contamination. For the widely employed methodologies (e.g. Graphical Lasso), using the sample covariance matrix as an input matrix potentially deteriorates the precision matrix estimation performance in the presence of outliers. We propose several robust alternatives for the covariance matrix, which are constructed by combining robust correlation estimators with robust variation measures. Through extensive numerical studies we demonstrate the robust performance of our proposed approaches compared to the standard methods based on the sample covariance matrix. Further, we apply our proposals to a real data application, aimed at studying the optimal portfolio allocations in Shanghai Stock Exchange Composite index. The results show that the proposed alternatives provide desirable out-of-sample performance.

Precision matrix estimation under data contamination with an application to minimum variance portfolio selection