Estimation of Sparse Variance-Covariance Matrix

This chapter discusses estimation of variance-covariance matrix with a focus on the case when the variance-covariance matrix is sparse. This is relevant in multi-dimensional panel because the number of possible specifications in the error components grows exponentially as the number of dimension increases and different specifications and independence assumptions lead to different sparsity structure of their variance-covariance matrix. Therefore it is possible to examine possible misspecification in the error components by leveraging specific sparsity structure of the variance-covariance matrix. This chapter demonstrates this possibility by proposing a new test statistic. Monte Carlo experiments show that the test perform well in finite sample.