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Statistical inference with high-dimensional data
Cun-Hui Zhang, Rutgers University

We consider a semi low-dimensional approach to statistical inference with highdimensional
data. The approach is best described with the following model statement:

model = low-dimensional component + high-dimensional component.

The main objective of this approach is to develop asymptotically efficient statistical
inference procedures for the low-dimensional component, such as p-values and confi-
dence regions. Just as in semiparametric inference, a sufficiently accurate estimate of
the high-dimensional component is required in order to carry out the inference for the
low-dimensional component. The feasibility of estimating the high-dimensional component
at the required accuracy depends on the model complexity and ill-posedness,
signal strength, the type of low-dimensional inference problem under consideration, and
sometimes availability of certain ancillary information. We will consider linear regression
and Gaussian graphical model as primary examples. We will describe concave penalized
methods which take advantage of partial signal strength, strategies and algorithms of debiasing
the Lasso and concave penalized estimators, the sample size requirement for the
de-biasing methods to work, and the contributions of unlabeled data in semi-supervised
regression.

Slides:
Zhang_lectures.pdf


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