Highdimensional Covariance Estimation

Estimating a covariance matrix is a basic task whenever many variables are measured together, whether the data come from markets, hospitals, factories, or field sciences. Pourahmadi's book surveys both the traditional techniques and the newer methods built for large, correlated datasets, and it shows how those methods connect to work in statistical learning.

The central material concerns three families of approaches: shrinkage, thresholding, and penalized likelihood. Each is applied to problems such as Gaussian graphical models, predictive modeling, and mean-variance portfolio construction. Throughout, the author explains many existing methods and algorithms through regression, which lets readers see how seemingly different procedures relate to one another.

The text is aimed at statisticians, mathematicians, economists, computer scientists, and engineers who work with high-dimensional data. It also suits graduate courses in multivariate analysis, covariance estimation, statistical learning, and high-dimensional data analysis, either as a main text or as a supplement.