This paper proposes a method for constructing a sparse estimator for the inverse covariance (concentration) matrix in high-dimensional settings. The estimator uses a penalized normal likelihood approach and forces sparsity by using a lasso-type penalty. The paper establishes a rate of convergence in the Frobenius norm as both data dimension p and sample size n grow, showing that the rate depends explicitly on how sparse the true concentration matrix is. It also shows that a correlation-based version of the method exhibits better rates in the operator norm. A fast iterative algorithm is derived for computing the estimator, which relies on the Cholesky decomposition of the inverse but produces a permutation-invariant estimator. The method is compared to other estimators on simulated data and on a real data example of tumor tissue classification using gene expression data. The paper analyzes the SPICE method, which is a sparse permutation invariant covariance estimator. It shows that the rate of convergence of the estimator depends on how sparse the true concentration matrix is. A modification of the method based on using the correlation matrix is also presented, which results in a better rate in the operator norm. The paper derives an optimization algorithm for computing the estimator based on Cholesky decomposition and local quadratic approximation. The algorithm is permutation-invariant and can be applied to general $ l_q $ penalties on the entries of the inverse. The paper also presents numerical results for SPICE and other methods on simulated data and a real example of tumor tissue classification using gene expression data. The results show that SPICE performs well in sparse models and outperforms other estimators in certain cases. The paper concludes that the SPICE method provides a useful tool for estimating sparse concentration matrices in high-dimensional settings.This paper proposes a method for constructing a sparse estimator for the inverse covariance (concentration) matrix in high-dimensional settings. The estimator uses a penalized normal likelihood approach and forces sparsity by using a lasso-type penalty. The paper establishes a rate of convergence in the Frobenius norm as both data dimension p and sample size n grow, showing that the rate depends explicitly on how sparse the true concentration matrix is. It also shows that a correlation-based version of the method exhibits better rates in the operator norm. A fast iterative algorithm is derived for computing the estimator, which relies on the Cholesky decomposition of the inverse but produces a permutation-invariant estimator. The method is compared to other estimators on simulated data and on a real data example of tumor tissue classification using gene expression data. The paper analyzes the SPICE method, which is a sparse permutation invariant covariance estimator. It shows that the rate of convergence of the estimator depends on how sparse the true concentration matrix is. A modification of the method based on using the correlation matrix is also presented, which results in a better rate in the operator norm. The paper derives an optimization algorithm for computing the estimator based on Cholesky decomposition and local quadratic approximation. The algorithm is permutation-invariant and can be applied to general $ l_q $ penalties on the entries of the inverse. The paper also presents numerical results for SPICE and other methods on simulated data and a real example of tumor tissue classification using gene expression data. The results show that SPICE performs well in sparse models and outperforms other estimators in certain cases. The paper concludes that the SPICE method provides a useful tool for estimating sparse concentration matrices in high-dimensional settings.