This paper proposes a unified framework to quantify local and global inferential uncertainty for high dimensional nonparanormal graphical models. In particular, we consider the problems of testing the presence of a single edge and constructing a uniform confidence subgraph. Due to the presence of unknown marginal transformations, we propose a pseudo likelihood based inferential approach. In sha...

I n the control of batch distillation columns, one of the problems is the difficulty in monitoring the compositions. This problem can be handled by estimating the compositions from readily available online temperature measurements using a state estimator. In this study, a state estimator that infers the product composition in a multicomponent batch distillation column (MBDC) from the temperatur...

In this paper, a comparison of linear and nonlinear estimators with particular emphasis to the closed-loop properties of the resulting inferential control scheme is presented. The concept of closed-loop “consistency” is introduced as an effective criterion for choosing the auxiliary variables. An estimator is consistent if it guarantees low closedloop steady-state offset in the true unmeasured ...

Carbon accounting is at the heart of efforts to mitigate the effects of climate change. One approach for estimating population parameters for live tree stem carbon entails three primary steps: (1) construction of an individual tree, allometric carbon model, (2) application of the model to tree-level data for a probability sample of plots, and (3) use of a probability-based (design-based) estima...

Inference for the mean of a normal distribution with known coefficient of variation is of special theoretical interest because the model belongs to the curved exponential family with a scalar parameter of interest and a two-dimensional minimal sufficient statistic. Therefore, standard inferential methods cannot be directly applied to this problem. It is also of practical interest because this p...

We provide a general theory of the expectation-maximization (EM) algorithm for inferring high dimensional latent variable models. In particular, we make two contributions: (i) For parameter estimation, we propose a novel high dimensional EM algorithm which naturally incorporates sparsity structure into parameter estimation. With an appropriate initialization, this algorithm converges at a geome...

We provide a general theory of the expectation-maximization (EM) algorithm for inferring high dimensional latent variable models. In particular, we make two contributions: (i) For parameter estimation, we propose a novel high dimensional EM algorithm which naturally incorporates sparsity structure into parameter estimation. With an appropriate initialization, this algorithm converges at a geome...

The assumptions underlying the Ordinary Least Squares (OLS) model are regularly and sometimes severely violated. In consequence, inferential procedures presumed valid for OLS are invalidated in practice. We describe a framework that is robust to model violations, and describe the modifications to the classical inferential procedures necessary to preserve inferential validity. As the covariates ...