Robust Covariance Matrix Estimation for High-Dimensional Compositional Data with Application to Sales Data Analysis

Danning Li, Arun Srinivasan, Qian Chen and Lingzhou Xue

Journal of Business & Economic Statistics, 2023, vol. 41, issue 4, 1090-1100

Abstract: Compositional data arises in a wide variety of research areas when some form of standardization and composition is necessary. Estimating covariance matrices is of fundamental importance for high-dimensional compositional data analysis. However, existing methods require the restrictive Gaussian or sub-Gaussian assumption, which may not hold in practice. We propose a robust composition adjusted thresholding covariance procedure based on Huber-type M-estimation to estimate the sparse covariance structure of high-dimensional compositional data. We introduce a cross-validation procedure to choose the tuning parameters of the proposed method. Theoretically, by assuming a bounded fourth moment condition, we obtain the rates of convergence and signal recovery property for the proposed method and provide the theoretical guarantees for the cross-validation procedure under the high-dimensional setting. Numerically, we demonstrate the effectiveness of the proposed method in simulation studies and also a real application to sales data analysis.

Date: 2023
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DOI: 10.1080/07350015.2022.2106990

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