proposed algorithm is very fast, efficient and easily scalable to a large scale data analysis problem.

The rest of the paper is organized as following. The next section highlights some background and problem set-up for covariance and inverse covariance matrix estimation. In section 3, we describe the proposed estimators and establish their theoretical consistency. In section 4, we give an algorithm and compare its computational time with some other existing algorithms. Section 5 highlights the performance of the proposed estimators on simulated data while an application of proposed estimator to real life data is given in section 6.

**Notation:** For a matrix $M$, let $\|M\|_1 $ denote its $\ell_1$ norm defined as the sum of absolute values of the entries of $M$, $\|M\|_F$ denote its Frobenius norm, defined as the sum of square of elements of $M$, $\|M\|$ denote its operator norm (also called spectral norm), defined as the largest absolute eigenvalue of $M$, $M^{-}$ denotes matrix $M$ where all diagonal elements are set to zero, $M^{+}$ denote matrix $M$ where all off-diagonal elements are set to zero, $\sigma_i(M)$ denote the $i^{th}$ largest eigenvalue of $M$, $tr(M)$ denotes its trace, $det(M)$ denote its determinant, $\sigma_{min}(M) $ and $\sigma_{max}(M)$ denote the 