High-dimensional mean estimation viaℓ1penalized normal likelihood

Mean likelihood frequency estimation

Estimation of signals with nonlinear as well as linear parameters in noise is studied. Maximum likelihood estimation has been shown to perform the best among all the methods. In such problems, joint maximum likelihood estimation of the unknown parameters reduces to a separable optimization problem, where first, the nonlinear parameters are estimated via a grid search, and then, the nonlinear pa...

Likelihood Ratio Tests for High-Dimensional Normal Distributions

In the paper by Jiang and Yang (2013), six classical Likelihood Ratio Test (LRT) statistics are studied under high-dimensional settings. Assuming that a random sample of size n is observed from a p-dimensional normal population, they derive the central limit theorems (CLTs) when p/n → y ∈ (0, 1], which are different from the classical chisquare limits as n goes to infinity while p remains fixed...

Maximum Likelihood for Variance Estimation in High-Dimensional Linear Models

The plots in Figure 1 from the main text were generated using various estimators of σ 0 , each of which was computed for 500 independent datasets (y, X). The datasets were generated according to the linear model (1)– (2) (equation references refer to the main text), with n = 500, p = 1000, σ 0 = 1, and η 2 0 = 4. We considered settings where β had various sparsity levels, indicated by a paramet...

Estimation of the Multivariate Normal Mean under the Extended Reflected Normal Loss Function

Modified Maximum Likelihood Estimation in First-Order Autoregressive Moving Average Models with some Non-Normal Residuals

When modeling time series data using autoregressive-moving average processes, it is a common practice to presume that the residuals are normally distributed. However, sometimes we encounter non-normal residuals and asymmetry of data marginal distribution. Despite widespread use of pure autoregressive processes for modeling non-normal time series, the autoregressive-moving average models have le...