This function returns a CI for an entries of interest with a significant level alpha
CI_mc(i, j, alpha = 0.05, missfrac, X.db, est_rank, sigma2 = 1)the row index of the interest entry X_i,j
the row index of the interest entry X_i,j
confidence level, default is 0.05
the missing proportion in the underlying matrix. It is the total of missing entries over total entries.
the de-biased estimated matrix from the 'dbmc' function.
the (estimated) low-rank of the underlying matrix or the rank of the de-biased estimator.
the noise-variance level.
CI confidence interval.
(i,j) the location of the entry at i-th row and j-th column.
v.ij the estimated variance of the limiting Gaussian distribution.
Chen et al (2019). Inference and uncertainty quantification for noisy matrix completion. PNAS, 116(46), 22931-22937.