CI_mc {dbMC}

compute the confidence intervals (CIs) from the de-biased estimator

Description

This function returns a CI for an entries of interest with a significant level alpha

Usage

CI_mc(i, j, alpha = 0.05, missfrac, X.db, est_rank, sigma2 = 1)

Arguments

i

the row index of the interest entry X_i,j

j

the row index of the interest entry X_i,j

alpha

confidence level, default is 0.05

missfrac

the missing proportion in the underlying matrix. It is the total of missing entries over total entries.

X.db

the de-biased estimated matrix from the 'dbmc' function.

est_rank

the (estimated) low-rank of the underlying matrix or the rank of the de-biased estimator.

sigma2

the noise-variance level.

Value

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.

References

Chen et al (2019). Inference and uncertainty quantification for noisy matrix completion. PNAS, 116(46), 22931-22937.