TY - JOUR
T1 - Robust Covariance Matrix Estimation for High-Dimensional Compositional Data with Application to Sales Data Analysis
AU - Li, Danning
AU - Srinivasan, Arun
AU - Chen, Qian
AU - Xue, Lingzhou
N1 - Funding Information:
Danning Li was partially supported by the National Natural Science Foundation of China grant 12101116. Arun Srinivasan and Lingzhou Xue were partially supported by the National Institutes of Health grants R21AI144765 and T32GM102057, and the National Science Foundation grants DMS-1811552 and DMS-1953189. We would like to thank the editor, associate editor and referees for their helpful comments and suggestions.
Publisher Copyright:
© 2022 American Statistical Association.
PY - 2023
Y1 - 2023
N2 - 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.
AB - 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.
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U2 - 10.1080/07350015.2022.2106990
DO - 10.1080/07350015.2022.2106990
M3 - Article
C2 - 38125739
AN - SCOPUS:85139021690
SN - 0735-0015
VL - 41
SP - 1090
EP - 1100
JO - Journal of Business and Economic Statistics
JF - Journal of Business and Economic Statistics
IS - 4
ER -