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Abstract:
This paper considers the minimax estimation of the high-dimensional sparse covariance matrices in the presence of missing observations. Based on random missing data, the upper bounds of convergence rate about the data-driven thresholding estimator are constructed over a large class of sparse covariance matrices under the l(1) norm and the Frobenius norm. In addition, we use Le Cam's lemma and the relation between the total variation affinity and the Kullback-Leibler divergence to establish the lower bounds which illustrate the desired upper bounds cannot be improved. It is worth mentioning that the approach we adopt to get the lower bounds is simpler than the existing ones.
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Source :
INTERNATIONAL JOURNAL OF WAVELETS MULTIRESOLUTION AND INFORMATION PROCESSING
ISSN: 0219-6913
Year: 2022
Issue: 06
Volume: 20
1 . 4
JCR@2022
1 . 4 0 0
JCR@2022
ESI Discipline: COMPUTER SCIENCE;
ESI HC Threshold:46
JCR Journal Grade:3
CAS Journal Grade:4
Cited Count:
SCOPUS Cited Count:
ESI Highly Cited Papers on the List: 0 Unfold All
WanFang Cited Count:
Chinese Cited Count:
30 Days PV: 1
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