A debiasing and spectral projection procedure constructs asymptotically normal estimators for any linear form of a low-rank matrix from noisy partial observations, enabling confidence intervals and tests.
Therefore, under the event of Theorem 4, ⏐⏐⟨ (ˆΘiˆΘT i − ΘΘT)A(ˆΘiˆΘT i − ΘΘT),~T ⟩⏐⏐ ≤C2κ0µ2 max‖T‖𝓁1σξ √ r2d1 logd1 n · σξ λr √ d2 1d2 logd1 n
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Statistical Inferences of Linear Forms for Noisy Matrix Completion
A debiasing and spectral projection procedure constructs asymptotically normal estimators for any linear form of a low-rank matrix from noisy partial observations, enabling confidence intervals and tests.