Ultrahigh dimensional precision matrix estimation via refitted cross validation

Variance estimation using refitted cross-validation in ultrahigh dimensional regression.

Variance estimation is a fundamental problem in statistical modelling. In ultrahigh dimensional linear regression where the dimensionality is much larger than the sample size, traditional variance estimation techniques are not applicable. Recent advances in variable selection in ultrahigh dimensional linear regression make this problem accessible. One of the major problems in ultrahigh dimensio...

Refitted Cross-validation in Ultrahigh Dimensional Regression

Variance estimation is a fundamental problem in statistical modeling. In ultrahigh dimensional linear regressions where the dimensionality is much larger than sample size, traditional variance estimation techniques are not applicable. Recent advances on variable selection in ultrahigh dimensional linear regressions make this problem more accessible. One of the major problems in ultrahigh dimens...

Expected Utility Estimation via Cross-Validation

We discuss practical methods for the assessment, comparison and selection of complex hierarchical Bayesian models. A natural way to assess the goodness of the model is to estimate its future predictive capability by estimating expected utilities. Instead of just making a point estimate, it is important to obtain the distribution of the expected utility estimate in order to describe the associat...

High Dimensional Multivariate Regression and Precision Matrix Estimation via Nonconvex Optimization

We propose a nonconvex estimator for joint multivariate regression and precision matrix estimation in the high dimensional regime, under sparsity constraints. A gradient descent algorithm with hard thresholding is developed to solve the nonconvex estimator, and it attains a linear rate of convergence to the true regression coefficients and precision matrix simultaneously, up to the statistical ...

Approaches to High-Dimensional Covariance and Precision Matrix Estimation