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Motivated by applications in high-dimensional data analysis where strong signals often stand out easily and weak ones may be indistinguishable from the noise, we develop a statistical framework to pro...
We study the problem of high-dimensional regression when there may be interacting vari-ables. We introduce a new idea called Backtracking, that can be incorporated into many existing high-dimensional ...
In many social, economical, biological and medical studies, one objective is to classify a subject into one of several classes based on a set of variables observed from the subject. Because the prob...
We show that scale-adjusted versions of the centroid-based classi- fier enjoys optimal properties when used to discriminate between two very high-dimensional populations where the principal differen...
We propose a two-sample test for the means of high-dimensional data when the data dimension is much larger than the sample size. Hotelling’s classical T 2 test does not work for this large p, small...
In this paper, we study inference for high-dimensional data characterized by small sample sizes relative to the dimension of the data. In particular, we provide an infinite-dimensional framework to ...
The estimation of Bayesian networks given high-dimensional data sets, in particular given gene expression data sets, has been the focus of much recent research. While there are many methods availabl...
Student's t statistic is nding applications today that were never envisaged when it was introduced more than a century ago. Many of these applications rely on properties, for example robustness aga...
In this paper, tests are developed for testing certain hypotheses on the covariance matrix Σ, when the sample size N = n + 1 is smaller than the dimension pof the data. Under the condition that (tr Σi...
In microarray experiments, the dimension p of the data is very large but there are only a few observations N on the subjects/patients. In this article, the problem of classifying a subject into one of...
In this article, we develop a multivariate theory for analyzing multivariate datasets that have fewer observations than dimensions. More specifically, we consider the problem of testing the hypothesis...
The Akaike information criterion (AIC) has been successfully used in the literature in model selection when there are a small number of parameters p and a large number of observations N. The cases whe...

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