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Statistical and computational trade-offs in estimation of sparse principal components
(Institute of Mathematical StatisticsAnnals of Statistics, 2016)
In recent years, Sparse Principal Component Analysis has emerged as an extremely popular dimension reduction technique for highdimensional data. The theoretical challenge, in the simplest case, is to estimate the leading ...
A Functional Approach to Deconvolve Dynamic Neuroimaging Data
(Taylor & FrancisJournal of the American Statistical Association, 2015-11-20)
Positron Emission Tomography (PET) is an imaging technique which can be used
to investigate chemical changes in human biological processes such as cancer development or neurochemical reactions. Most dynamic PET scans are ...
Generalised additive and index models with shape constraints
(WileyJournal of the Royal Statistical Society: Series B (Statistical Methodology), 2015-10-26)
We study generalized additive models, with shape restrictions (e.g. monotonicity, convexity and concavity) imposed on each component of the additive prediction function. We show that this framework facilitates a non-parametric ...
On the motive of some hyperKaehler varieties
(De GruyterJournal für die reine und angewandte Mathematik, 2015-06-05)
We show that the motive of the Hilbert scheme of length-n subschemes on a K3 surface or on an abelian surface admits a decomposition similar to the decomposition of the motive of an abelian variety obtained by Shermenev, ...
Transversals as Generating Sets in Finitely Generated Groups
(Cambridge University PressBulletin of the Australian Mathematical Society, 2015-08-19)
We explore transversals of finite index subgroups of finitely generated groups. We show that when H is a subgroup of a rank n group G and H has index at least n in G then we can construct a left transversal for H which ...
Near-optimal estimation of jump activity in semimartingales
(Institute of Mathematical StatisticsThe Annals of Statistics, 2015-07-15)
In quantitative finance, we often model asset prices as semimartingales, with drift, diffusion and jump components. The jump activity index measures the strength of the jumps at high frequencies, and is of interest both ...
F-Saturation Games
(ElsevierDiscrete Mathematics, 2015-06-23)
We study F-saturation games, first introduced by Füredi, Reimer and Seress [4] in 1991, and named as such by West [5]. The main question is to determine the length of the game whilst avoiding various classes of graph, ...
Deformations of Cayley submanifolds
(University of CambridgeDepartment of Pure Mathematics and Mathematical StatisticsTrinity College, 2016-03-01)
Cayley submanifolds of R^8 were introduced by Harvey and Lawson as an instance of calibrated submanifolds, extending the volume-minimising properties of complex submanifolds in Kähler manifolds. More generally, Cayley ...
Chaos and Entropic Chaos in Kac's Model Without High Moments
(Institute of Mathematical StatisticsElectronic Journal of Probability, 2013-08-27)
In this paper we present a new local Lévy Central Limit Theorem, showing convergence to stable states that are not necessarily the Gaussian, and use it to find new and intuitive entropically chaotic families with underlying ...