TY  - JOUR
A1  - Carpentier, Alexandra
A1  - Kim, Arlene K. H.
T1  - An iterative hard thresholding estimator for low rank matrix recovery with explicit limiting distribution
JF  - Statistica Sinica
N2  - We consider the problem of low rank matrix recovery in a stochastically noisy high-dimensional setting. We propose a new estimator for the low rank matrix, based on the iterative hard thresholding method, that is computationally efficient and simple. We prove that our estimator is optimal in terms of the Frobenius risk and in terms of the entry-wise risk uniformly over any change of orthonormal basis, allowing us to provide the limiting distribution of the estimator. When the design is Gaussian, we prove that the entry-wise bias of the limiting distribution of the estimator is small, which is of interest for constructing tests and confidence sets for low-dimensional subsets of entries of the low rank matrix.
KW  - High dimensional statistical inference
KW  - inverse problem
KW  - limiting distribution
KW  - low rank matrix recovery
KW  - numerical methods
KW  - uncertainty quantification
Y1  - 2018
U6  - https://doi.org/10.5705/ss.202016.0103
SN  - 1017-0405
SN  - 1996-8507
VL  - 28
IS  - 3
SP  - 1371
EP  - 1393
PB  - Statistica Sinica, Institute of Statistical Science, Academia Sinica
CY  - Taipei
ER  -