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A useful variant of the Davis--Kahan theorem for statisticians
The Davis–Kahan theorem is used in the analysis of many statistical procedures to bound the distance between subspaces spanned by population eigenvectors and their sample versions. It relies on anExpand
Variable selection with error control: another look at stability selection
Summary. Stability selection was recently introduced by Meinshausen and Buhlmann as a very general technique designed to improve the performance of a variable selection algorithm. It is based onExpand
Ultrahigh Dimensional Feature Selection: Beyond The Linear Model
In this paper, we extend ISIS, without explicit definition of residuals, to a general pseudo-likelihood framework, which includes generalized linear models as a special case. Expand
High-dimensional changepoint estimation via sparse projection
Changepoints are a very common feature of Big Data that arrive in the form of a data stream. In this paper, we study high-dimensional time series in which, at certain time points, the mean structureExpand
Neogene overflow of Northern Component Water at the Greenland‐Scotland Ridge
In the North Atlantic Ocean, flow of North Atlantic Deep Water (NADW), and of its ancient counterpart Northern Component Water (NCW), across the Greenland-Scotland Ridge (GSR) is thought to haveExpand
Optimal weighted nearest neighbour classifiers
We derive an asymptotic expansion for the excess risk (regret) of a weighted nearest-neighbour classifier. This allows us to find the asymptotically optimal vector of nonnegative weights, which has aExpand
Efficient multivariate entropy estimation via $k$-nearest neighbour distances
Many statistical procedures, including goodness-of-fit tests and methods for independent component analysis, rely critically on the estimation of the entropy of a distribution. In this paper, we seekExpand
Theoretical properties of the log-concave maximum likelihood estimator of a multidimensional density
We present theoretical properties of the log-concave maximum likelihood estimator of a density based on an independent and identically distributed sample in R d . Our study covers both the case whereExpand
Maximum likelihood estimation of a multidimensional log-concave density
Let X_1, ..., X_n be independent and identically distributed random vectors with a log-concave (Lebesgue) density f. We first prove that, with probability one, there exists a unique maximumExpand